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

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