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Introductory Exercise 30.1
Ques 1: The wavelength for n = 3 to n = 2 transition of the hydrogen 
atom is 656.3 nm. What are the wavelengths for this same transition 
in
(a) positronium, which consists of an electron and a positron
(b) singly ionized helium (Note: A positron is a positively charged 
electron).
Sol: (a) Reduced mass of positronium and electron is m/2 where m = mass of 
electron)
m has become half, so ? will become two times or 1312 nm or 1.31 nm.
For singly ionized helium atom z = 2
? 
Ques 2: Find the longest wavelength present in the Balmer series of 
hydrogen.
Sol: Longest wavelength, means minimum energy.
Ques 3: (a) Find the frequencies of revolution of electrons in n = 1 and 
n = 2 Bohr orbits. (b) What is the frequency of the photon emitted 
when an electron in an n = 2 orbit drops to an n = 1 hydrogen orbit?
(c) An electron typically spends about 10-8s in an excited state before 
Page 2


Introductory Exercise 30.1
Ques 1: The wavelength for n = 3 to n = 2 transition of the hydrogen 
atom is 656.3 nm. What are the wavelengths for this same transition 
in
(a) positronium, which consists of an electron and a positron
(b) singly ionized helium (Note: A positron is a positively charged 
electron).
Sol: (a) Reduced mass of positronium and electron is m/2 where m = mass of 
electron)
m has become half, so ? will become two times or 1312 nm or 1.31 nm.
For singly ionized helium atom z = 2
? 
Ques 2: Find the longest wavelength present in the Balmer series of 
hydrogen.
Sol: Longest wavelength, means minimum energy.
Ques 3: (a) Find the frequencies of revolution of electrons in n = 1 and 
n = 2 Bohr orbits. (b) What is the frequency of the photon emitted 
when an electron in an n = 2 orbit drops to an n = 1 hydrogen orbit?
(c) An electron typically spends about 10-8s in an excited state before 
it drops to a lower state by emitting a photon. How many revolutions 
does an electron in an n = 2 Bohr hydrogen orbit make in 1.00 × 10-
8 s?
Sol:
? 
(b) ?E =E2 - E1 = 10.2 eV = hf
= 6.47 × 1015Hz
(c) In option (a), we have found that,
Ques 4: A muon is an unstable elementary particle whose mass is 207 
me and whose charge is either +e or-e. A negative muon (µ-) can be 
captured by a nucleus to form a muonic atom.
(a) A proton captures a µ-. Find the radius of the first Bohr orbit of 
this atom.
(b) Find the ionization energy of the atom.
Note Attempt this question after reading the whole chapter.
Page 3


Introductory Exercise 30.1
Ques 1: The wavelength for n = 3 to n = 2 transition of the hydrogen 
atom is 656.3 nm. What are the wavelengths for this same transition 
in
(a) positronium, which consists of an electron and a positron
(b) singly ionized helium (Note: A positron is a positively charged 
electron).
Sol: (a) Reduced mass of positronium and electron is m/2 where m = mass of 
electron)
m has become half, so ? will become two times or 1312 nm or 1.31 nm.
For singly ionized helium atom z = 2
? 
Ques 2: Find the longest wavelength present in the Balmer series of 
hydrogen.
Sol: Longest wavelength, means minimum energy.
Ques 3: (a) Find the frequencies of revolution of electrons in n = 1 and 
n = 2 Bohr orbits. (b) What is the frequency of the photon emitted 
when an electron in an n = 2 orbit drops to an n = 1 hydrogen orbit?
(c) An electron typically spends about 10-8s in an excited state before 
it drops to a lower state by emitting a photon. How many revolutions 
does an electron in an n = 2 Bohr hydrogen orbit make in 1.00 × 10-
8 s?
Sol:
? 
(b) ?E =E2 - E1 = 10.2 eV = hf
= 6.47 × 1015Hz
(c) In option (a), we have found that,
Ques 4: A muon is an unstable elementary particle whose mass is 207 
me and whose charge is either +e or-e. A negative muon (µ-) can be 
captured by a nucleus to form a muonic atom.
(a) A proton captures a µ-. Find the radius of the first Bohr orbit of 
this atom.
(b) Find the ionization energy of the atom.
Note Attempt this question after reading the whole chapter.
Sol: 
?  
= 2.55 × 10-13 m
(b) E ? m
? Ionization energy of given atom =
(m) (ionization energy of hydrogen atom)
= (207) (13.6 eV) = 2815.2 eV= 2.81 keV
Ques 5: Find the de-Broglie wavelengths of
(a) a 46 g golf ball with a velocity of 30 m/s,
(b) an electron with a velocity of 107 m/s.
Sol:
Ques 6: (a) A gas of hydrogen atoms in their ground state is 
bombarded by electrons with kinetic energy 12.5 eV. What emitted 
wavelengths would you expect to see?
(b) What if the electrons were replaced by photons of same energy?
Sol: (a) En -E1 = 12.5
? 
Solving we get, n = 3.51
Hence electron jumps to n = 3.
So possible lines are between n = 3 to n = 2, n = 3 to n = 1 and between n = 2 
Page 4


Introductory Exercise 30.1
Ques 1: The wavelength for n = 3 to n = 2 transition of the hydrogen 
atom is 656.3 nm. What are the wavelengths for this same transition 
in
(a) positronium, which consists of an electron and a positron
(b) singly ionized helium (Note: A positron is a positively charged 
electron).
Sol: (a) Reduced mass of positronium and electron is m/2 where m = mass of 
electron)
m has become half, so ? will become two times or 1312 nm or 1.31 nm.
For singly ionized helium atom z = 2
? 
Ques 2: Find the longest wavelength present in the Balmer series of 
hydrogen.
Sol: Longest wavelength, means minimum energy.
Ques 3: (a) Find the frequencies of revolution of electrons in n = 1 and 
n = 2 Bohr orbits. (b) What is the frequency of the photon emitted 
when an electron in an n = 2 orbit drops to an n = 1 hydrogen orbit?
(c) An electron typically spends about 10-8s in an excited state before 
it drops to a lower state by emitting a photon. How many revolutions 
does an electron in an n = 2 Bohr hydrogen orbit make in 1.00 × 10-
8 s?
Sol:
? 
(b) ?E =E2 - E1 = 10.2 eV = hf
= 6.47 × 1015Hz
(c) In option (a), we have found that,
Ques 4: A muon is an unstable elementary particle whose mass is 207 
me and whose charge is either +e or-e. A negative muon (µ-) can be 
captured by a nucleus to form a muonic atom.
(a) A proton captures a µ-. Find the radius of the first Bohr orbit of 
this atom.
(b) Find the ionization energy of the atom.
Note Attempt this question after reading the whole chapter.
Sol: 
?  
= 2.55 × 10-13 m
(b) E ? m
? Ionization energy of given atom =
(m) (ionization energy of hydrogen atom)
= (207) (13.6 eV) = 2815.2 eV= 2.81 keV
Ques 5: Find the de-Broglie wavelengths of
(a) a 46 g golf ball with a velocity of 30 m/s,
(b) an electron with a velocity of 107 m/s.
Sol:
Ques 6: (a) A gas of hydrogen atoms in their ground state is 
bombarded by electrons with kinetic energy 12.5 eV. What emitted 
wavelengths would you expect to see?
(b) What if the electrons were replaced by photons of same energy?
Sol: (a) En -E1 = 12.5
? 
Solving we get, n = 3.51
Hence electron jumps to n = 3.
So possible lines are between n = 3 to n = 2, n = 3 to n = 1 and between n = 2 
to n = 1.
For n = 3 to n = 2
? 
Similarly other wavelengths can also be obtained.
(b) n = 3.51 (in option-a)
A photon always transfers its energy completely.
So it cannot excite the ground state electrons to n = 3 (like and electrons 
excited it in part-a).
Ques 7: For a given element the wavelength of the Ka line is 0.71 nm 
and of the Kß line it is 0.63 nm. Use this information to find 
wavelength of the La line.
Sol:
Ques 8: The energy of the n = 2 state in a given element is E2 = - 2870 
eV. Given that the wavelengths of the Ka and Kß lines are 0.71 nm 
Page 5


Introductory Exercise 30.1
Ques 1: The wavelength for n = 3 to n = 2 transition of the hydrogen 
atom is 656.3 nm. What are the wavelengths for this same transition 
in
(a) positronium, which consists of an electron and a positron
(b) singly ionized helium (Note: A positron is a positively charged 
electron).
Sol: (a) Reduced mass of positronium and electron is m/2 where m = mass of 
electron)
m has become half, so ? will become two times or 1312 nm or 1.31 nm.
For singly ionized helium atom z = 2
? 
Ques 2: Find the longest wavelength present in the Balmer series of 
hydrogen.
Sol: Longest wavelength, means minimum energy.
Ques 3: (a) Find the frequencies of revolution of electrons in n = 1 and 
n = 2 Bohr orbits. (b) What is the frequency of the photon emitted 
when an electron in an n = 2 orbit drops to an n = 1 hydrogen orbit?
(c) An electron typically spends about 10-8s in an excited state before 
it drops to a lower state by emitting a photon. How many revolutions 
does an electron in an n = 2 Bohr hydrogen orbit make in 1.00 × 10-
8 s?
Sol:
? 
(b) ?E =E2 - E1 = 10.2 eV = hf
= 6.47 × 1015Hz
(c) In option (a), we have found that,
Ques 4: A muon is an unstable elementary particle whose mass is 207 
me and whose charge is either +e or-e. A negative muon (µ-) can be 
captured by a nucleus to form a muonic atom.
(a) A proton captures a µ-. Find the radius of the first Bohr orbit of 
this atom.
(b) Find the ionization energy of the atom.
Note Attempt this question after reading the whole chapter.
Sol: 
?  
= 2.55 × 10-13 m
(b) E ? m
? Ionization energy of given atom =
(m) (ionization energy of hydrogen atom)
= (207) (13.6 eV) = 2815.2 eV= 2.81 keV
Ques 5: Find the de-Broglie wavelengths of
(a) a 46 g golf ball with a velocity of 30 m/s,
(b) an electron with a velocity of 107 m/s.
Sol:
Ques 6: (a) A gas of hydrogen atoms in their ground state is 
bombarded by electrons with kinetic energy 12.5 eV. What emitted 
wavelengths would you expect to see?
(b) What if the electrons were replaced by photons of same energy?
Sol: (a) En -E1 = 12.5
? 
Solving we get, n = 3.51
Hence electron jumps to n = 3.
So possible lines are between n = 3 to n = 2, n = 3 to n = 1 and between n = 2 
to n = 1.
For n = 3 to n = 2
? 
Similarly other wavelengths can also be obtained.
(b) n = 3.51 (in option-a)
A photon always transfers its energy completely.
So it cannot excite the ground state electrons to n = 3 (like and electrons 
excited it in part-a).
Ques 7: For a given element the wavelength of the Ka line is 0.71 nm 
and of the Kß line it is 0.63 nm. Use this information to find 
wavelength of the La line.
Sol:
Ques 8: The energy of the n = 2 state in a given element is E2 = - 2870 
eV. Given that the wavelengths of the Ka and Kß lines are 0.71 nm 
and 0.63 nm, respectively determine the energies E1 and E3.
Sol: 
E1 =E2 - 1743 = -2870 - 1743 = 4613 eV
= 1964 eV
? E3 = E1 + 1964
= -4613+1964 = -2649 eV
Ques 9: The energy levels of a certain atom are shown in figure. If a 
photon of frequency f is emitted when there is an electron transition 
from 5E to E, what frequencies of photons could be produced by 
other energy level transitions?
Sol: 5E - E = hf
? ...(i)
Between 5E and 4E
5E - 4E = hf1
?  (from eq. (i))
Between 4E and E
4E - E = hf2
?  
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FAQs on DC Pandey Solutions: Modern Physics I - Physics Class 12 - NEET

1. What are DC Pandey Solutions?
Ans. DC Pandey Solutions are the detailed explanations and solved examples of the problems given in the book "DC Pandey Modern Physics I". These solutions help students understand the concepts and techniques required to solve the physics problems in the book.
2. How can I use DC Pandey Solutions to prepare for the Modern Physics I exam?
Ans. To prepare for the Modern Physics I exam using DC Pandey Solutions, you can refer to the solutions provided for each problem in the book. These solutions will guide you step-by-step on how to approach and solve the problems. By practicing these solutions, you can improve your problem-solving skills and gain a better understanding of the concepts.
3. Are the DC Pandey Solutions for Modern Physics I available online?
Ans. Yes, DC Pandey Solutions for Modern Physics I are available online. You can find them on various educational websites, forums, or even on the official website of DC Pandey. These solutions are typically available in the form of PDF files or as part of online study materials.
4. Are the DC Pandey Solutions reliable for exam preparation?
Ans. Yes, DC Pandey Solutions are considered reliable for exam preparation. The solutions provided in the book are well-explained and follow a logical approach to solving the problems. By practicing these solutions, you can develop a good understanding of the concepts and improve your problem-solving skills, which will ultimately help you in the exam.
5. Can I solely rely on DC Pandey Solutions for Modern Physics I exam preparation?
Ans. While DC Pandey Solutions are a valuable resource for exam preparation, it is recommended not to solely rely on them. It is important to supplement your preparation with other study materials, textbooks, and practice tests to get a comprehensive understanding of the subject. Additionally, consulting with teachers or joining coaching classes can provide further guidance and clarification on any doubts or concepts.
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