DC Pandey Solutions: Modern Physics I - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE

JEE: DC Pandey Solutions: Modern Physics I - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE

The document DC Pandey Solutions: Modern Physics I - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE is a part of the JEE Course DC Pandey Solutions for JEE Physics.
All you need of JEE at this link: JEE

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)
DC Pandey Solutions: Modern Physics I - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE
m has become half, so λ will become two times or 1312 nm or 1.31 nm.
DC Pandey Solutions: Modern Physics I - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE
For singly ionized helium atom z = 2
DC Pandey Solutions: Modern Physics I - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE

Ques 2: Find the longest wavelength present in the Balmer series of hydrogen.
Sol:
Longest wavelength, means minimum energy.
DC Pandey Solutions: Modern Physics I - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE

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:
DC Pandey Solutions: Modern Physics I - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE
DC Pandey Solutions: Modern Physics I - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE
DC Pandey Solutions: Modern Physics I - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE
(b) ΔE =E2 - E1 = 10.2 eV = hf
DC Pandey Solutions: Modern Physics I - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE
= 6.47 × 1015Hz
(c) In option (a), we have found that,
DC Pandey Solutions: Modern Physics I - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE

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: DC Pandey Solutions: Modern Physics I - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE

∴  DC Pandey Solutions: Modern Physics I - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE
= 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:

DC Pandey Solutions: Modern Physics I - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE

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
DC Pandey Solutions: Modern Physics I - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE
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
DC Pandey Solutions: Modern Physics I - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE
DC Pandey Solutions: Modern Physics I - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE
DC Pandey Solutions: Modern Physics I - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE
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 Kα line is 0.71 nm and of the Kβ line it is 0.63 nm. Use this information to find wavelength of the Lα line.
Sol:

DC Pandey Solutions: Modern Physics I - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE
DC Pandey Solutions: Modern Physics I - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE

Ques 8: The energy of the n = 2 state in a given element is E2 = - 2870 eV. Given that the wavelengths of the Kα and Kβ lines are 0.71 nm and 0.63 nm, respectively determine the energies E1 and E3.
Sol: 
DC Pandey Solutions: Modern Physics I - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE
DC Pandey Solutions: Modern Physics I - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE
E1 =E2 - 1743 = -2870 - 1743 = 4613 eV
DC Pandey Solutions: Modern Physics I - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE
DC Pandey Solutions: Modern Physics I - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE
= 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?
DC Pandey Solutions: Modern Physics I - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE
Sol:
5E - E = hf
DC Pandey Solutions: Modern Physics I - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE...(i)
Between 5E and 4E
5E - 4E = hf1
DC Pandey Solutions: Modern Physics I - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE (from eq. (i))
Between 4E and E
4E - E = hf2
DC Pandey Solutions: Modern Physics I - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE 

The document DC Pandey Solutions: Modern Physics I - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE is a part of the JEE Course DC Pandey Solutions for JEE Physics.
All you need of JEE at this link: JEE

Related Searches

Extra Questions

,

DC Pandey Solutions: Modern Physics I - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE

,

practice quizzes

,

video lectures

,

Free

,

Objective type Questions

,

Semester Notes

,

study material

,

mock tests for examination

,

MCQs

,

past year papers

,

Exam

,

Previous Year Questions with Solutions

,

shortcuts and tricks

,

DC Pandey Solutions: Modern Physics I - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE

,

Viva Questions

,

ppt

,

Summary

,

DC Pandey Solutions: Modern Physics I - 1 Notes | Study DC Pandey Solutions for JEE Physics - JEE

,

pdf

,

Important questions

,

Sample Paper

;