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Page 1
Exercises
For JEE Main
Subjective Questions
Note You can take approximations in the answers.
h = 6.62 × 10
-34
J-s, c = 3.0 × 10
8
m/s, m
e
=9.1 × 10
-31
kg and 1 eV = 1.6 × 10
-19
J
Electromagnetic Waves
Q 1. Find the energy, the mass and the momentum of a photon of ultraviolet radiation of 280 nm
wavelength.
Q 2. A small plate of a metal is placed at a distance of 2 m from a monochromatic light source of
wavelength 4.8 × 10
-7
m and power 1.0 watt. The light falls normally on the plate. Find the
number of photons striking the metal plate per square metre per second.
Q 3. A photon has momentum of magnitude 8.24 × 10
-28
kg-m/s.
(a) What is the energy of this photon? Give your answer in joules and in electron volts.
(b) What is the wavelength of this photon? In what region of the electromagnetic spectrum does it
lay?
Q 4. A 75 W light source emits light of wavelength 600 nm.
(a) Calculate the frequency of the emitted light.
(b) How many photons per second does the source emit?
Q 5. An excited nucleus emits a gamma-ray photon with energy of 2.45 MeV.
(a) What is the photon frequency? (b) What is the photon wavelength?
Q 6. (a) A proton is moving at a speed much less than the speed of light. It has kinetic energy K
1
and
momentum p
1
. If the momentum of the proton is doubled, so p
2
= 2p
1
, how is its new kinetic
energy K
2
related to K
1
?
(b) A photon with energy E
1
has momentum p
1
. If another photon has momentum p
2
that is twice
p
1
, how is the energy E
2
of the second photon related to E
1
?
Momentum and Radiation Pressure
Q 7. A parallel beam of monochromatic light of wavelength 500 nm is incident normally on a perfectly
absorbing surface. The power through any cross-section of the beam is 10 W. Find
(a) the number of photons absorbed per second by the surface and
(b) the force exerted by the light beam on the surface.
Q 8. A beam of white light is incident normally on a plane surface absorbing 70% of the light and
reflecting the rest. If the incident beam carries 10 W of power, find the force exerted by it on the
surface.
Q 9. A parallel beam of monochromatic light of wavelength 663 nm is incident on a totally reflecting
plane mirror. The angle of incidence is 60° and the number of photons striking the mirror per
second is 1.0 × 10
19
. Calculate the force exerted by the light beam on the mirror.
Q 10. A 100 W light bulb is placed at the centre of a spherical chamber of radius 20 cm. Assume that
60% of the energy supplied to the bulb is converted into light and that the surface of the chamber
is perfectly absorbing. Find the pressure exerted by the light on the surface of the chamber.
de-Broglie Wavelength
Page 2
Exercises
For JEE Main
Subjective Questions
Note You can take approximations in the answers.
h = 6.62 × 10
-34
J-s, c = 3.0 × 10
8
m/s, m
e
=9.1 × 10
-31
kg and 1 eV = 1.6 × 10
-19
J
Electromagnetic Waves
Q 1. Find the energy, the mass and the momentum of a photon of ultraviolet radiation of 280 nm
wavelength.
Q 2. A small plate of a metal is placed at a distance of 2 m from a monochromatic light source of
wavelength 4.8 × 10
-7
m and power 1.0 watt. The light falls normally on the plate. Find the
number of photons striking the metal plate per square metre per second.
Q 3. A photon has momentum of magnitude 8.24 × 10
-28
kg-m/s.
(a) What is the energy of this photon? Give your answer in joules and in electron volts.
(b) What is the wavelength of this photon? In what region of the electromagnetic spectrum does it
lay?
Q 4. A 75 W light source emits light of wavelength 600 nm.
(a) Calculate the frequency of the emitted light.
(b) How many photons per second does the source emit?
Q 5. An excited nucleus emits a gamma-ray photon with energy of 2.45 MeV.
(a) What is the photon frequency? (b) What is the photon wavelength?
Q 6. (a) A proton is moving at a speed much less than the speed of light. It has kinetic energy K
1
and
momentum p
1
. If the momentum of the proton is doubled, so p
2
= 2p
1
, how is its new kinetic
energy K
2
related to K
1
?
(b) A photon with energy E
1
has momentum p
1
. If another photon has momentum p
2
that is twice
p
1
, how is the energy E
2
of the second photon related to E
1
?
Momentum and Radiation Pressure
Q 7. A parallel beam of monochromatic light of wavelength 500 nm is incident normally on a perfectly
absorbing surface. The power through any cross-section of the beam is 10 W. Find
(a) the number of photons absorbed per second by the surface and
(b) the force exerted by the light beam on the surface.
Q 8. A beam of white light is incident normally on a plane surface absorbing 70% of the light and
reflecting the rest. If the incident beam carries 10 W of power, find the force exerted by it on the
surface.
Q 9. A parallel beam of monochromatic light of wavelength 663 nm is incident on a totally reflecting
plane mirror. The angle of incidence is 60° and the number of photons striking the mirror per
second is 1.0 × 10
19
. Calculate the force exerted by the light beam on the mirror.
Q 10. A 100 W light bulb is placed at the centre of a spherical chamber of radius 20 cm. Assume that
60% of the energy supplied to the bulb is converted into light and that the surface of the chamber
is perfectly absorbing. Find the pressure exerted by the light on the surface of the chamber.
de-Broglie Wavelength
Q 11. Wavelength of Bullet. Calculate the de-Broglie wavelength of a 5.00 g bullet that is moving at 340
m/s. Will it exhibit wave like properties?
Q 12. (a) An electron moves with a speed of 4.70 × 10
6
m/s. What is its de-Broglie wavelength? (b) A
proton moves with the same speed. Determine its de-Broglie wavelength.
Q 13. An electron has a de-Broglie wavelength of 2.80 × 10
-10
m. Determine
(a) the magnitude of its momentum,
(b) its kinetic energy (in joule and in electron volt).
Q 14. Find de-Broglie wavelength corresponding to the root-mean square velocity of hydrogen
molecules at room temperature (20°C).
Q 15. An electron, in a hydrogen-like atom, is in excited state. It has a total energy of-3.4 eV, find the
de-Broglie wavelength of the electron.
Q 16. In the Bohr model of the hydrogen atom, what is the de-Broglie wavelength for the electron when
it is in
(a) the n = 1 level?
(b) the n = 4 level? In each case, compare the de-Broglie wavelength to the circumference 2 ?r
n
of
the orbit.
Bohr's Atomic Model and Emission Spectrum
Q 17. Find the ionization energy of a doubly ionized lithium atom.
Q 18. The total energy of an electron in the first excited state of the hydrogen atom is -3.4 eV.
(a) What is the kinetic energy of the electron in this state?
(b) What is the potential energy of the electron in this state?
(c) Which of the answers above would change if the choice of the zero of potential energy is
changed?
Q 19. The binding energy of an electron in the ground state of He atom is equal to E
0
= 24.6 eV Find the
energy required to remove both electrons from the atom.
Q 20. A hydrogen atom is in a state with energy -1.51 eV In the Bohr model, what is the angular
momentum of the electron in the atom, with respect to an axis at the nucleus?
Q 21. Hydrogen atom in its ground state is excited by means of monochromatic radiation of wavelength
1023 Å. How many different lines are possible in the resulting spectrum? Calculate the longest
wavelength among them. You may assume the ionization energy of hydrogen atom as 13.6 eV.
Q 22. A doubly ionized lithium atom is hydrogen-like with atomic number 3. Find the wavelength of the
radiation require to excite the electron in Li
++
from the first to the third Bohr orbit (ionization
energy of the hydrogen atom equals 13.6 eV).
Q 23. Find the quantum number n corresponding to nth excited state of He
+
ion if on transition to the
ground state the ion emits two photons in succession with wavelengths 108.5 nm and 30.4 nm.
The ionization energy of the hydrogen atom is 13.6 eV.
Q 24. A hydrogen like atom (described by the Bohr model) is observed to emit ten wavelengths,
originating from all possible transitions between a group of levels. These levels have energies
between -0.85 eV and -0.544 eV (including both these values).
(a) Find the atomic number of the atom.
Page 3
Exercises
For JEE Main
Subjective Questions
Note You can take approximations in the answers.
h = 6.62 × 10
-34
J-s, c = 3.0 × 10
8
m/s, m
e
=9.1 × 10
-31
kg and 1 eV = 1.6 × 10
-19
J
Electromagnetic Waves
Q 1. Find the energy, the mass and the momentum of a photon of ultraviolet radiation of 280 nm
wavelength.
Q 2. A small plate of a metal is placed at a distance of 2 m from a monochromatic light source of
wavelength 4.8 × 10
-7
m and power 1.0 watt. The light falls normally on the plate. Find the
number of photons striking the metal plate per square metre per second.
Q 3. A photon has momentum of magnitude 8.24 × 10
-28
kg-m/s.
(a) What is the energy of this photon? Give your answer in joules and in electron volts.
(b) What is the wavelength of this photon? In what region of the electromagnetic spectrum does it
lay?
Q 4. A 75 W light source emits light of wavelength 600 nm.
(a) Calculate the frequency of the emitted light.
(b) How many photons per second does the source emit?
Q 5. An excited nucleus emits a gamma-ray photon with energy of 2.45 MeV.
(a) What is the photon frequency? (b) What is the photon wavelength?
Q 6. (a) A proton is moving at a speed much less than the speed of light. It has kinetic energy K
1
and
momentum p
1
. If the momentum of the proton is doubled, so p
2
= 2p
1
, how is its new kinetic
energy K
2
related to K
1
?
(b) A photon with energy E
1
has momentum p
1
. If another photon has momentum p
2
that is twice
p
1
, how is the energy E
2
of the second photon related to E
1
?
Momentum and Radiation Pressure
Q 7. A parallel beam of monochromatic light of wavelength 500 nm is incident normally on a perfectly
absorbing surface. The power through any cross-section of the beam is 10 W. Find
(a) the number of photons absorbed per second by the surface and
(b) the force exerted by the light beam on the surface.
Q 8. A beam of white light is incident normally on a plane surface absorbing 70% of the light and
reflecting the rest. If the incident beam carries 10 W of power, find the force exerted by it on the
surface.
Q 9. A parallel beam of monochromatic light of wavelength 663 nm is incident on a totally reflecting
plane mirror. The angle of incidence is 60° and the number of photons striking the mirror per
second is 1.0 × 10
19
. Calculate the force exerted by the light beam on the mirror.
Q 10. A 100 W light bulb is placed at the centre of a spherical chamber of radius 20 cm. Assume that
60% of the energy supplied to the bulb is converted into light and that the surface of the chamber
is perfectly absorbing. Find the pressure exerted by the light on the surface of the chamber.
de-Broglie Wavelength
Q 11. Wavelength of Bullet. Calculate the de-Broglie wavelength of a 5.00 g bullet that is moving at 340
m/s. Will it exhibit wave like properties?
Q 12. (a) An electron moves with a speed of 4.70 × 10
6
m/s. What is its de-Broglie wavelength? (b) A
proton moves with the same speed. Determine its de-Broglie wavelength.
Q 13. An electron has a de-Broglie wavelength of 2.80 × 10
-10
m. Determine
(a) the magnitude of its momentum,
(b) its kinetic energy (in joule and in electron volt).
Q 14. Find de-Broglie wavelength corresponding to the root-mean square velocity of hydrogen
molecules at room temperature (20°C).
Q 15. An electron, in a hydrogen-like atom, is in excited state. It has a total energy of-3.4 eV, find the
de-Broglie wavelength of the electron.
Q 16. In the Bohr model of the hydrogen atom, what is the de-Broglie wavelength for the electron when
it is in
(a) the n = 1 level?
(b) the n = 4 level? In each case, compare the de-Broglie wavelength to the circumference 2 ?r
n
of
the orbit.
Bohr's Atomic Model and Emission Spectrum
Q 17. Find the ionization energy of a doubly ionized lithium atom.
Q 18. The total energy of an electron in the first excited state of the hydrogen atom is -3.4 eV.
(a) What is the kinetic energy of the electron in this state?
(b) What is the potential energy of the electron in this state?
(c) Which of the answers above would change if the choice of the zero of potential energy is
changed?
Q 19. The binding energy of an electron in the ground state of He atom is equal to E
0
= 24.6 eV Find the
energy required to remove both electrons from the atom.
Q 20. A hydrogen atom is in a state with energy -1.51 eV In the Bohr model, what is the angular
momentum of the electron in the atom, with respect to an axis at the nucleus?
Q 21. Hydrogen atom in its ground state is excited by means of monochromatic radiation of wavelength
1023 Å. How many different lines are possible in the resulting spectrum? Calculate the longest
wavelength among them. You may assume the ionization energy of hydrogen atom as 13.6 eV.
Q 22. A doubly ionized lithium atom is hydrogen-like with atomic number 3. Find the wavelength of the
radiation require to excite the electron in Li
++
from the first to the third Bohr orbit (ionization
energy of the hydrogen atom equals 13.6 eV).
Q 23. Find the quantum number n corresponding to nth excited state of He
+
ion if on transition to the
ground state the ion emits two photons in succession with wavelengths 108.5 nm and 30.4 nm.
The ionization energy of the hydrogen atom is 13.6 eV.
Q 24. A hydrogen like atom (described by the Bohr model) is observed to emit ten wavelengths,
originating from all possible transitions between a group of levels. These levels have energies
between -0.85 eV and -0.544 eV (including both these values).
(a) Find the atomic number of the atom.
(b) Calculate the smallest wavelength emitted in these transitions.
(Take ground state energy of hydrogen atom = -13.6eV)
Q 25. The energy levels of a hypothetical one electron atom are shown in the figure.
(a) Find the ionization potential of this atom.
(b) Find the short wavelength limit of the series terminating at n = 2
(c) Find the excitation potential for the state n = 3.
(d) Find wave number of the photon emitted for the transition n = 3 to n = 1
Q 26. (a) An atom initially in an energy level with E = - 6.52 eV absorbs a photon that has wavelength
860 nm. What is the internal energy of the atom after it absorbs the photon?
(b) An atom initially in an energy level with E = - 2.68 eVemits a photon that has wavelength 420
nm. What is the internal energy of the atom after it emits the photon?
Q 27. A small particle of mass m moves in such a way that the potential energy
2 2 2
1
U m r
2
?? where ? is
a constant and r is the distance of the particle from the origin. Assuming Bohr's model of
quantization of angular momentum and circular orbits, show that radius of the nth allowed orbit is
proportional to n .
X-Rays
Q 28. Wavelength of K
?
line of an element is ?
0
.
Find wavelength of K
?
line for the same element.
Q 29. X-rays are produced in an X-ray tube by electrons accelerated through an electric potential
difference of 50.0 kV. An electron makes three collisions in the target coming to rest and loses
half its remaining kinetic energy in each of the first two collisions. Determine the wavelength of
the resulting photons. (Neglecting the recoil of the heavy target atoms).
Q 30. From what material is the anode of an X-ray tube made, if the K
?
-line wavelength of the
characteristic spectrum is 0.76Å ?
Q 31. A voltage applied to an X -ray tube being increased ? = 1.5
times, the short wave limit of an X-ray
continuous spectrum shifts by ? ? = 26 pm Find the initial voltage applied to the tube.
Q 32. The K
?
X-rays of aluminium (Z=13) and zinc (Z=30) have wavelengths 887 pm and 146pm
respectively. Use Moseley's equation v = a(Z - b) to find the wavelength of the K
?
X-ray of iron
(Z = 26)
Q 33. Characteristic X-ray of frequency 4.2 x 10
18
Hz are produced when transitions from L shell take
place in a certain target material. Use Moseley's law and determine the atomic number of the
target material. Given Rydberg constant R = 1.1 × 10
7
m
-1
.
Q 34. The electric current in an X-ray tube operating at 40 kV is 10 mA. Assume that on an average 1 %
of the total kinetic energy of the electrons hitting the target are converted into X-rays.
Page 4
Exercises
For JEE Main
Subjective Questions
Note You can take approximations in the answers.
h = 6.62 × 10
-34
J-s, c = 3.0 × 10
8
m/s, m
e
=9.1 × 10
-31
kg and 1 eV = 1.6 × 10
-19
J
Electromagnetic Waves
Q 1. Find the energy, the mass and the momentum of a photon of ultraviolet radiation of 280 nm
wavelength.
Q 2. A small plate of a metal is placed at a distance of 2 m from a monochromatic light source of
wavelength 4.8 × 10
-7
m and power 1.0 watt. The light falls normally on the plate. Find the
number of photons striking the metal plate per square metre per second.
Q 3. A photon has momentum of magnitude 8.24 × 10
-28
kg-m/s.
(a) What is the energy of this photon? Give your answer in joules and in electron volts.
(b) What is the wavelength of this photon? In what region of the electromagnetic spectrum does it
lay?
Q 4. A 75 W light source emits light of wavelength 600 nm.
(a) Calculate the frequency of the emitted light.
(b) How many photons per second does the source emit?
Q 5. An excited nucleus emits a gamma-ray photon with energy of 2.45 MeV.
(a) What is the photon frequency? (b) What is the photon wavelength?
Q 6. (a) A proton is moving at a speed much less than the speed of light. It has kinetic energy K
1
and
momentum p
1
. If the momentum of the proton is doubled, so p
2
= 2p
1
, how is its new kinetic
energy K
2
related to K
1
?
(b) A photon with energy E
1
has momentum p
1
. If another photon has momentum p
2
that is twice
p
1
, how is the energy E
2
of the second photon related to E
1
?
Momentum and Radiation Pressure
Q 7. A parallel beam of monochromatic light of wavelength 500 nm is incident normally on a perfectly
absorbing surface. The power through any cross-section of the beam is 10 W. Find
(a) the number of photons absorbed per second by the surface and
(b) the force exerted by the light beam on the surface.
Q 8. A beam of white light is incident normally on a plane surface absorbing 70% of the light and
reflecting the rest. If the incident beam carries 10 W of power, find the force exerted by it on the
surface.
Q 9. A parallel beam of monochromatic light of wavelength 663 nm is incident on a totally reflecting
plane mirror. The angle of incidence is 60° and the number of photons striking the mirror per
second is 1.0 × 10
19
. Calculate the force exerted by the light beam on the mirror.
Q 10. A 100 W light bulb is placed at the centre of a spherical chamber of radius 20 cm. Assume that
60% of the energy supplied to the bulb is converted into light and that the surface of the chamber
is perfectly absorbing. Find the pressure exerted by the light on the surface of the chamber.
de-Broglie Wavelength
Q 11. Wavelength of Bullet. Calculate the de-Broglie wavelength of a 5.00 g bullet that is moving at 340
m/s. Will it exhibit wave like properties?
Q 12. (a) An electron moves with a speed of 4.70 × 10
6
m/s. What is its de-Broglie wavelength? (b) A
proton moves with the same speed. Determine its de-Broglie wavelength.
Q 13. An electron has a de-Broglie wavelength of 2.80 × 10
-10
m. Determine
(a) the magnitude of its momentum,
(b) its kinetic energy (in joule and in electron volt).
Q 14. Find de-Broglie wavelength corresponding to the root-mean square velocity of hydrogen
molecules at room temperature (20°C).
Q 15. An electron, in a hydrogen-like atom, is in excited state. It has a total energy of-3.4 eV, find the
de-Broglie wavelength of the electron.
Q 16. In the Bohr model of the hydrogen atom, what is the de-Broglie wavelength for the electron when
it is in
(a) the n = 1 level?
(b) the n = 4 level? In each case, compare the de-Broglie wavelength to the circumference 2 ?r
n
of
the orbit.
Bohr's Atomic Model and Emission Spectrum
Q 17. Find the ionization energy of a doubly ionized lithium atom.
Q 18. The total energy of an electron in the first excited state of the hydrogen atom is -3.4 eV.
(a) What is the kinetic energy of the electron in this state?
(b) What is the potential energy of the electron in this state?
(c) Which of the answers above would change if the choice of the zero of potential energy is
changed?
Q 19. The binding energy of an electron in the ground state of He atom is equal to E
0
= 24.6 eV Find the
energy required to remove both electrons from the atom.
Q 20. A hydrogen atom is in a state with energy -1.51 eV In the Bohr model, what is the angular
momentum of the electron in the atom, with respect to an axis at the nucleus?
Q 21. Hydrogen atom in its ground state is excited by means of monochromatic radiation of wavelength
1023 Å. How many different lines are possible in the resulting spectrum? Calculate the longest
wavelength among them. You may assume the ionization energy of hydrogen atom as 13.6 eV.
Q 22. A doubly ionized lithium atom is hydrogen-like with atomic number 3. Find the wavelength of the
radiation require to excite the electron in Li
++
from the first to the third Bohr orbit (ionization
energy of the hydrogen atom equals 13.6 eV).
Q 23. Find the quantum number n corresponding to nth excited state of He
+
ion if on transition to the
ground state the ion emits two photons in succession with wavelengths 108.5 nm and 30.4 nm.
The ionization energy of the hydrogen atom is 13.6 eV.
Q 24. A hydrogen like atom (described by the Bohr model) is observed to emit ten wavelengths,
originating from all possible transitions between a group of levels. These levels have energies
between -0.85 eV and -0.544 eV (including both these values).
(a) Find the atomic number of the atom.
(b) Calculate the smallest wavelength emitted in these transitions.
(Take ground state energy of hydrogen atom = -13.6eV)
Q 25. The energy levels of a hypothetical one electron atom are shown in the figure.
(a) Find the ionization potential of this atom.
(b) Find the short wavelength limit of the series terminating at n = 2
(c) Find the excitation potential for the state n = 3.
(d) Find wave number of the photon emitted for the transition n = 3 to n = 1
Q 26. (a) An atom initially in an energy level with E = - 6.52 eV absorbs a photon that has wavelength
860 nm. What is the internal energy of the atom after it absorbs the photon?
(b) An atom initially in an energy level with E = - 2.68 eVemits a photon that has wavelength 420
nm. What is the internal energy of the atom after it emits the photon?
Q 27. A small particle of mass m moves in such a way that the potential energy
2 2 2
1
U m r
2
?? where ? is
a constant and r is the distance of the particle from the origin. Assuming Bohr's model of
quantization of angular momentum and circular orbits, show that radius of the nth allowed orbit is
proportional to n .
X-Rays
Q 28. Wavelength of K
?
line of an element is ?
0
.
Find wavelength of K
?
line for the same element.
Q 29. X-rays are produced in an X-ray tube by electrons accelerated through an electric potential
difference of 50.0 kV. An electron makes three collisions in the target coming to rest and loses
half its remaining kinetic energy in each of the first two collisions. Determine the wavelength of
the resulting photons. (Neglecting the recoil of the heavy target atoms).
Q 30. From what material is the anode of an X-ray tube made, if the K
?
-line wavelength of the
characteristic spectrum is 0.76Å ?
Q 31. A voltage applied to an X -ray tube being increased ? = 1.5
times, the short wave limit of an X-ray
continuous spectrum shifts by ? ? = 26 pm Find the initial voltage applied to the tube.
Q 32. The K
?
X-rays of aluminium (Z=13) and zinc (Z=30) have wavelengths 887 pm and 146pm
respectively. Use Moseley's equation v = a(Z - b) to find the wavelength of the K
?
X-ray of iron
(Z = 26)
Q 33. Characteristic X-ray of frequency 4.2 x 10
18
Hz are produced when transitions from L shell take
place in a certain target material. Use Moseley's law and determine the atomic number of the
target material. Given Rydberg constant R = 1.1 × 10
7
m
-1
.
Q 34. The electric current in an X-ray tube operating at 40 kV is 10 mA. Assume that on an average 1 %
of the total kinetic energy of the electrons hitting the target are converted into X-rays.
(a) What is the total power emitted as X-rays and
(b) How much heat is produced in the target every second?
Photoelectric Effect
Q 35. The stopping potential for the photoelectrons emitted from a metal surface of work function 1.7
eV is 10.4 V. Find the wavelength of the radiation used. Also identity the energy levels in
hydrogen atom, which will emit this wavelength.
Q 36. What will be the maximum kinetic energy of the photoelectrons ejected from magnesium (for
which the work function W = 3.7eV) when irradiated by ultraviolet light of frequency 1.5 × 10
15
sec
-1
.
Q 37. A metallic surface is irradiated with monochromatic light of variable wavelength. Above a
wavelength of 5000 Å, no photoelectrons are emitted from the surface. With an unknown
wavelength, stopping potential of 3 V is necessary to eliminate the photo-current. Find the
unknown wavelength.
Q 38. A graph regarding photoelectric effect is shown between the maximum kinetic energy of electrons
and the frequency of the incident light. On the basis of data as shown in the graph, calculate :
(a) Threshold frequency, (b) Work function, (c) Planck's constant
Q 39. A metallic surface is illuminated alternatively with light of wavelengths 3000Å and 6000Å. It is
observed that the maximum speeds of the photoelectrons under these illuminations are in the ratio
3:1. Calculate the work function of the metal and the maximum speed of the photoelectrons in two
cases.
Q 40. When a beam of 10.6 eV photons of intensity 2.0 Wm
-2
falls on aplatinum surface of area 1.0 ×
10
-4
m
2
and work function 5.6 eV, 0.53% of the incident photons eject photoelectrons. Find the
number of photoelectrons emitted per second and their minimum and maximum energies (in eV).
Q 41. Light of wavelength 180 nm ejects photoelectrons from a plate of metal whose work function is 2
eV. If a uniform magnetic field of 5 × 10
-5
T be applied parallel to the plate, what would be the
radius of the path followed by electrons ejected normally from the plate with maximum energy.
Q 42. Light described at a place by the equation E = (100 V/m) [sin(5 × 10
15
s
-1
)t + sin(8 × 10
15
s
-1
)t]
falls on a metal surface having work function 2.0 eV. Calculate the maximum kinetic energy of the
photoelectrons.
Q 43. The electric field associated with a light wave is given by E =E
0
sin [(1.57 × 10
7
m
-1
)(x - ct)].
Find the stopping potential when this light is used in an experiment on photoelectric effect with
the similar having work function 1.9 eV.
Solutions
Page 5
Exercises
For JEE Main
Subjective Questions
Note You can take approximations in the answers.
h = 6.62 × 10
-34
J-s, c = 3.0 × 10
8
m/s, m
e
=9.1 × 10
-31
kg and 1 eV = 1.6 × 10
-19
J
Electromagnetic Waves
Q 1. Find the energy, the mass and the momentum of a photon of ultraviolet radiation of 280 nm
wavelength.
Q 2. A small plate of a metal is placed at a distance of 2 m from a monochromatic light source of
wavelength 4.8 × 10
-7
m and power 1.0 watt. The light falls normally on the plate. Find the
number of photons striking the metal plate per square metre per second.
Q 3. A photon has momentum of magnitude 8.24 × 10
-28
kg-m/s.
(a) What is the energy of this photon? Give your answer in joules and in electron volts.
(b) What is the wavelength of this photon? In what region of the electromagnetic spectrum does it
lay?
Q 4. A 75 W light source emits light of wavelength 600 nm.
(a) Calculate the frequency of the emitted light.
(b) How many photons per second does the source emit?
Q 5. An excited nucleus emits a gamma-ray photon with energy of 2.45 MeV.
(a) What is the photon frequency? (b) What is the photon wavelength?
Q 6. (a) A proton is moving at a speed much less than the speed of light. It has kinetic energy K
1
and
momentum p
1
. If the momentum of the proton is doubled, so p
2
= 2p
1
, how is its new kinetic
energy K
2
related to K
1
?
(b) A photon with energy E
1
has momentum p
1
. If another photon has momentum p
2
that is twice
p
1
, how is the energy E
2
of the second photon related to E
1
?
Momentum and Radiation Pressure
Q 7. A parallel beam of monochromatic light of wavelength 500 nm is incident normally on a perfectly
absorbing surface. The power through any cross-section of the beam is 10 W. Find
(a) the number of photons absorbed per second by the surface and
(b) the force exerted by the light beam on the surface.
Q 8. A beam of white light is incident normally on a plane surface absorbing 70% of the light and
reflecting the rest. If the incident beam carries 10 W of power, find the force exerted by it on the
surface.
Q 9. A parallel beam of monochromatic light of wavelength 663 nm is incident on a totally reflecting
plane mirror. The angle of incidence is 60° and the number of photons striking the mirror per
second is 1.0 × 10
19
. Calculate the force exerted by the light beam on the mirror.
Q 10. A 100 W light bulb is placed at the centre of a spherical chamber of radius 20 cm. Assume that
60% of the energy supplied to the bulb is converted into light and that the surface of the chamber
is perfectly absorbing. Find the pressure exerted by the light on the surface of the chamber.
de-Broglie Wavelength
Q 11. Wavelength of Bullet. Calculate the de-Broglie wavelength of a 5.00 g bullet that is moving at 340
m/s. Will it exhibit wave like properties?
Q 12. (a) An electron moves with a speed of 4.70 × 10
6
m/s. What is its de-Broglie wavelength? (b) A
proton moves with the same speed. Determine its de-Broglie wavelength.
Q 13. An electron has a de-Broglie wavelength of 2.80 × 10
-10
m. Determine
(a) the magnitude of its momentum,
(b) its kinetic energy (in joule and in electron volt).
Q 14. Find de-Broglie wavelength corresponding to the root-mean square velocity of hydrogen
molecules at room temperature (20°C).
Q 15. An electron, in a hydrogen-like atom, is in excited state. It has a total energy of-3.4 eV, find the
de-Broglie wavelength of the electron.
Q 16. In the Bohr model of the hydrogen atom, what is the de-Broglie wavelength for the electron when
it is in
(a) the n = 1 level?
(b) the n = 4 level? In each case, compare the de-Broglie wavelength to the circumference 2 ?r
n
of
the orbit.
Bohr's Atomic Model and Emission Spectrum
Q 17. Find the ionization energy of a doubly ionized lithium atom.
Q 18. The total energy of an electron in the first excited state of the hydrogen atom is -3.4 eV.
(a) What is the kinetic energy of the electron in this state?
(b) What is the potential energy of the electron in this state?
(c) Which of the answers above would change if the choice of the zero of potential energy is
changed?
Q 19. The binding energy of an electron in the ground state of He atom is equal to E
0
= 24.6 eV Find the
energy required to remove both electrons from the atom.
Q 20. A hydrogen atom is in a state with energy -1.51 eV In the Bohr model, what is the angular
momentum of the electron in the atom, with respect to an axis at the nucleus?
Q 21. Hydrogen atom in its ground state is excited by means of monochromatic radiation of wavelength
1023 Å. How many different lines are possible in the resulting spectrum? Calculate the longest
wavelength among them. You may assume the ionization energy of hydrogen atom as 13.6 eV.
Q 22. A doubly ionized lithium atom is hydrogen-like with atomic number 3. Find the wavelength of the
radiation require to excite the electron in Li
++
from the first to the third Bohr orbit (ionization
energy of the hydrogen atom equals 13.6 eV).
Q 23. Find the quantum number n corresponding to nth excited state of He
+
ion if on transition to the
ground state the ion emits two photons in succession with wavelengths 108.5 nm and 30.4 nm.
The ionization energy of the hydrogen atom is 13.6 eV.
Q 24. A hydrogen like atom (described by the Bohr model) is observed to emit ten wavelengths,
originating from all possible transitions between a group of levels. These levels have energies
between -0.85 eV and -0.544 eV (including both these values).
(a) Find the atomic number of the atom.
(b) Calculate the smallest wavelength emitted in these transitions.
(Take ground state energy of hydrogen atom = -13.6eV)
Q 25. The energy levels of a hypothetical one electron atom are shown in the figure.
(a) Find the ionization potential of this atom.
(b) Find the short wavelength limit of the series terminating at n = 2
(c) Find the excitation potential for the state n = 3.
(d) Find wave number of the photon emitted for the transition n = 3 to n = 1
Q 26. (a) An atom initially in an energy level with E = - 6.52 eV absorbs a photon that has wavelength
860 nm. What is the internal energy of the atom after it absorbs the photon?
(b) An atom initially in an energy level with E = - 2.68 eVemits a photon that has wavelength 420
nm. What is the internal energy of the atom after it emits the photon?
Q 27. A small particle of mass m moves in such a way that the potential energy
2 2 2
1
U m r
2
?? where ? is
a constant and r is the distance of the particle from the origin. Assuming Bohr's model of
quantization of angular momentum and circular orbits, show that radius of the nth allowed orbit is
proportional to n .
X-Rays
Q 28. Wavelength of K
?
line of an element is ?
0
.
Find wavelength of K
?
line for the same element.
Q 29. X-rays are produced in an X-ray tube by electrons accelerated through an electric potential
difference of 50.0 kV. An electron makes three collisions in the target coming to rest and loses
half its remaining kinetic energy in each of the first two collisions. Determine the wavelength of
the resulting photons. (Neglecting the recoil of the heavy target atoms).
Q 30. From what material is the anode of an X-ray tube made, if the K
?
-line wavelength of the
characteristic spectrum is 0.76Å ?
Q 31. A voltage applied to an X -ray tube being increased ? = 1.5
times, the short wave limit of an X-ray
continuous spectrum shifts by ? ? = 26 pm Find the initial voltage applied to the tube.
Q 32. The K
?
X-rays of aluminium (Z=13) and zinc (Z=30) have wavelengths 887 pm and 146pm
respectively. Use Moseley's equation v = a(Z - b) to find the wavelength of the K
?
X-ray of iron
(Z = 26)
Q 33. Characteristic X-ray of frequency 4.2 x 10
18
Hz are produced when transitions from L shell take
place in a certain target material. Use Moseley's law and determine the atomic number of the
target material. Given Rydberg constant R = 1.1 × 10
7
m
-1
.
Q 34. The electric current in an X-ray tube operating at 40 kV is 10 mA. Assume that on an average 1 %
of the total kinetic energy of the electrons hitting the target are converted into X-rays.
(a) What is the total power emitted as X-rays and
(b) How much heat is produced in the target every second?
Photoelectric Effect
Q 35. The stopping potential for the photoelectrons emitted from a metal surface of work function 1.7
eV is 10.4 V. Find the wavelength of the radiation used. Also identity the energy levels in
hydrogen atom, which will emit this wavelength.
Q 36. What will be the maximum kinetic energy of the photoelectrons ejected from magnesium (for
which the work function W = 3.7eV) when irradiated by ultraviolet light of frequency 1.5 × 10
15
sec
-1
.
Q 37. A metallic surface is irradiated with monochromatic light of variable wavelength. Above a
wavelength of 5000 Å, no photoelectrons are emitted from the surface. With an unknown
wavelength, stopping potential of 3 V is necessary to eliminate the photo-current. Find the
unknown wavelength.
Q 38. A graph regarding photoelectric effect is shown between the maximum kinetic energy of electrons
and the frequency of the incident light. On the basis of data as shown in the graph, calculate :
(a) Threshold frequency, (b) Work function, (c) Planck's constant
Q 39. A metallic surface is illuminated alternatively with light of wavelengths 3000Å and 6000Å. It is
observed that the maximum speeds of the photoelectrons under these illuminations are in the ratio
3:1. Calculate the work function of the metal and the maximum speed of the photoelectrons in two
cases.
Q 40. When a beam of 10.6 eV photons of intensity 2.0 Wm
-2
falls on aplatinum surface of area 1.0 ×
10
-4
m
2
and work function 5.6 eV, 0.53% of the incident photons eject photoelectrons. Find the
number of photoelectrons emitted per second and their minimum and maximum energies (in eV).
Q 41. Light of wavelength 180 nm ejects photoelectrons from a plate of metal whose work function is 2
eV. If a uniform magnetic field of 5 × 10
-5
T be applied parallel to the plate, what would be the
radius of the path followed by electrons ejected normally from the plate with maximum energy.
Q 42. Light described at a place by the equation E = (100 V/m) [sin(5 × 10
15
s
-1
)t + sin(8 × 10
15
s
-1
)t]
falls on a metal surface having work function 2.0 eV. Calculate the maximum kinetic energy of the
photoelectrons.
Q 43. The electric field associated with a light wave is given by E =E
0
sin [(1.57 × 10
7
m
-1
)(x - ct)].
Find the stopping potential when this light is used in an experiment on photoelectric effect with
the similar having work function 1.9 eV.
Solutions
1.
2. Number of photons emitted per second,
At
a distance r, these photons are falling on an area 4 ?r
2
.
? Number of photons incident per unit area per unit time,
3. (a)
(b)
? 804 nm
? This wavelength lies in ultraviolet region.
4. (a)
(b) See the hint of Q.2 of same section.
? 2.3 × 10
20
photons/s
5. (a) E = hf
(b)
6. (a)
If momentum is doubled, kinetic energy becomes four times.
(b) (for a photon)
If P is doubled, E will also become two times.
7. (a) Number of photons incident per second = number of photons absorbed per second
(b) Force = Rate of change of momentum = (Number of photons absorbed per second) x
(momentum of one photon)
(P = power)
Read More
FAQs on DC Pandey Solutions (JEE Main): Modern Physics- I - DC Pandey Solutions for JEE Physics
| 1. What is Modern Physics and how is it relevant to the JEE Main Physics exam? |  |
Ans. Modern Physics is a branch of physics that deals with the study of the fundamental particles and their interactions, as well as the behavior of matter and energy at the atomic and subatomic level. It includes topics such as quantum mechanics, relativity, particle physics, and nuclear physics.
In the JEE Main Physics exam, Modern Physics is an important topic that carries significant weightage in terms of marks. Questions related to topics like photoelectric effect, atomic structure, nuclear reactions, and quantum mechanics are frequently asked. Therefore, a strong understanding of Modern Physics is essential for scoring well in the exam.
| 2. What are the key concepts to focus on while studying Modern Physics for the JEE Main exam? | |
Ans. While studying Modern Physics for the JEE Main exam, it is crucial to focus on the following key concepts:
- Quantum Mechanics: Understand the wave-particle duality, Heisenberg's uncertainty principle, wave functions, and probability density.
- Photoelectric Effect: Familiarize yourself with the concept of photons, work function, stopping potential, and Einstein's photoelectric equation.
- Atomic Structure: Learn about Bohr's model of the atom, energy levels, electronic configurations, and spectral lines.
- Nuclear Physics: Gain knowledge about nuclear reactions, radioactive decay, half-life, binding energy, and nuclear fission and fusion.
- Relativity: Grasp the basic principles of special relativity, time dilation, length contraction, and mass-energy equivalence.
Having a clear understanding of these concepts will enable you to solve a wide range of questions related to Modern Physics in the JEE Main exam.
| 3. How can I effectively prepare for Modern Physics in the JEE Main exam? | |
Ans. To effectively prepare for Modern Physics in the JEE Main exam, follow these tips:
1. Understand the Concepts: Start by thoroughly understanding the fundamental concepts and principles of Modern Physics. Refer to reliable textbooks and study materials to build a strong foundation.
2. Practice Numerical Problems: Modern Physics involves solving numerical problems. Practice a variety of numerical problems to develop problem-solving skills and familiarize yourself with the application of concepts.
3. Solve Previous Year Question Papers: Solve previous year question papers to get an idea of the exam pattern and the type of questions asked. This will also help you identify your weak areas and work on improving them.
4. Take Mock Tests: Regularly take mock tests to assess your preparation level and identify areas that require more focus. This will also help you improve your time management skills.
5. Seek Clarification: If you come across any doubts or concepts that are difficult to understand, don't hesitate to seek clarification from your teachers, peers, or online resources.
By following these tips and maintaining a consistent study schedule, you can effectively prepare for Modern Physics in the JEE Main exam.
| 4. Are there any specific formulas or equations that I should memorize for Modern Physics in the JEE Main exam? | |
Ans. Yes, there are several important formulas and equations that you should memorize for Modern Physics in the JEE Main exam. Some of these include:
- Einstein's Photoelectric Equation: E = hf = Φ + K.E. (where E is the energy of a photon, h is Planck's constant, f is the frequency of incident light, Φ is the work function, and K.E. is the kinetic energy of the emitted electron)
- De Broglie Wavelength: λ = h/p (where λ is the De Broglie wavelength, h is Planck's constant, and p is the momentum of a particle)
- Bohr's Frequency Condition: ΔE = hf (where ΔE is the change in energy of an electron, and f is the frequency of emitted or absorbed radiation)
- Energy of a Photon: E = hf (where E is the energy of a photon, h is Planck's constant, and f is the frequency of the photon)
- Relativistic Energy-Momentum Relationship: E^2 = (mc^2)^2 + (pc)^2 (where E is the total energy of a particle, m is its rest mass, c is the speed of light, and p is its momentum)
It is important to understand the derivation and application of these formulas and equations to solve problems related to Modern Physics in the JEE Main exam.
| 5. Can you recommend any additional study resources for Modern Physics in the JEE Main exam? | |
Ans. Along with the DC Pandey JEE Main Physics book, here are some additional study resources that can help you in preparing for Modern Physics:
- "Concepts of Modern Physics" by Arthur Beiser: This book provides a comprehensive coverage of the concepts of Modern Physics and includes numerous solved examples and practice questions.
- "Problems in General Physics" by I.E. Irodov: This book contains a wide range of challenging problems in Modern Physics, which can help you enhance your problem-solving skills.
- Online video lectures: Platforms like Khan Academy, NPTEL, and YouTube offer free video lectures on Modern Physics by renowned professors. These lectures can provide you with a different perspective and help clarify difficult concepts.
- JEE Main Previous Year Question Papers: Solve previous year question papers to get acquainted with the exam pattern and practice solving different types of questions related to Modern Physics.
Remember, while using additional study resources, always prioritize understanding the concepts and practicing problem-solving rather than relying solely on memorization.
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