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Phy1008_of_GOENKA_2025, Exercises of Physics

PHY1008_IMPORTANT QUESTIONS BANK.pdf

Typology: Exercises

2024/2025

Available from 04/17/2025

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Phy1008 Question Bank
UNIT-1
Short Questions
1. What does constant h represent?
2. Define the term photoelectric effect?
3. What are photo electrons?
4. What do you mean by work function of a metal?
5. Briefly define the Max Plank’s Hypothesis?
6. What is threshold frequency of radiations in reference of photoelectric effect?
7. On what factors does the mass of a photon depend.
8. Define the matter waves/de-Broglie waves?
9. Out of photon and electron, which one will have more speed if both have same
wavelength?
10. Define Heisenberg’s Uncertainty Principle.
11. Differentiate between phase velocity & group velocity.
12. Discuss some properties of photon.
13. Why electrons cannot exist inside the nucleus.
14. What are the conditions satisfied by the wave function.
15. Explain the physical significance of the wave function.
16. What are the limitations of the wave function.
17. What do you understand by free particle.
18. What are the characteristics or properties of a photon.
19. Out of photon and electron which have more speed if both have same wavelength.
20. Discuss energy time uncertainty principle.
Long Questions/Numerical
1. Give a description of failures of classical theory.
2. Explain dual nature of matter (or) wave particle duality.
3. What are de-Broglie waves? Show that the de-Broglie wavelength of a particle of
momentum p is h/p?
4. Differentiate between classical and quantum mechanics.
5. Explain Planck’s Quantum Hypothesis to explain the observed spectrum of a black
body radiation.
6. Explain in detail Rayleigh Jeans law and Wien’s Displacement Law.
7. Derive einstein photoelectric equation and explain the laws of photoelectric emission
with the help of this equation.
8. Assume an e⁻ in a hydrogen atom has a velocity of approximately 2.2 × 10⁶ m/s. Mass
of e⁻ is 9.109 × 10⁻³¹ kg. Calculate de-Broglie wavelength of an e⁻.
9. Consider a baseball with a mass of 0.15 kg travelling at 40 m/s. Calculate de-Broglie
wavelength.
10. The work function of sodium metal is 3.3 eV. What is the longest wavelength of light
that can cause photoelectric emission from sodium?
11. Calculate the de-Broglie wavelength of neutron of energy 28.8 eV. Given mass of
neutron m = 1.67 × 10⁻²⁷ kg.
12. Calculate the de-Broglie wavelength of α-particle accelerated through a potential
difference of 2000 V. Given mass of α-particle = 6.68 × 10⁻²⁷ kg.
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Phy1008 Question Bank

UNIT- 1

Short Questions

  1. What does constant h represent?
  2. Define the term photoelectric effect?
  3. What are photo electrons?
  4. What do you mean by work function of a metal?
  5. Briefly define the Max Plank’s Hypothesis?
  6. What is threshold frequency of radiations in reference of photoelectric effect?
  7. On what factors does the mass of a photon depend.
  8. Define the matter waves/de-Broglie waves?
  9. Out of photon and electron, which one will have more speed if both have same

wavelength?

  1. Define Heisenberg’s Uncertainty Principle.
  2. Differentiate between phase velocity & group velocity.
  3. Discuss some properties of photon.
  4. Why electrons cannot exist inside the nucleus.
  5. What are the conditions satisfied by the wave function.
  6. Explain the physical significance of the wave function.
  7. What are the limitations of the wave function.
  8. What do you understand by free particle.
  9. What are the characteristics or properties of a photon.
  10. Out of photon and electron which have more speed if both have same wavelength.
  11. Discuss energy time uncertainty principle.

Long Questions/Numerical

  1. Give a description of failures of classical theory.
  2. Explain dual nature of matter (or) wave particle duality.
  3. What are de-Broglie waves? Show that the de-Broglie wavelength of a particle of

momentum p is h/p?

  1. Differentiate between classical and quantum mechanics.
  2. Explain Planck’s Quantum Hypothesis to explain the observed spectrum of a black

body radiation.

  1. Explain in detail Rayleigh Jeans law and Wien’s Displacement Law.
  2. Derive einstein photoelectric equation and explain the laws of photoelectric emission

with the help of this equation.

  1. Assume an e⁻ in a hydrogen atom has a velocity of approximately 2.2 × 10⁶ m/s. Mass

of e⁻ is 9.109 × 10⁻³¹ kg. Calculate de-Broglie wavelength of an e⁻.

  1. Consider a baseball with a mass of 0.15 kg travelling at 40 m/s. Calculate de-Broglie

wavelength.

  1. The work function of sodium metal is 3.3 eV. What is the longest wavelength of light

that can cause photoelectric emission from sodium?

  1. Calculate the de-Broglie wavelength of neutron of energy 28.8 eV. Given mass of

neutron m = 1.67 × 10⁻²⁷ kg.

  1. Calculate the de-Broglie wavelength of α-particle accelerated through a potential

difference of 2000 V. Given mass of α-particle = 6.68 × 10⁻²⁷ kg.

  1. Calculate the de-Broglie wavelength of thermal neutrons at 21°C.
  2. Calculate the wavelength associated with an e⁻ subjected to a potential diff. of 1.

volt.

  1. An e⁻ & proton have same de-Broglie velocity. Prove that K.E of e⁻ is greater than

that of proton.

  1. Normalize the wave fnⁿ ψ(x) = A e

⁻(α|x|).

  1. Calculate Probability current density of ψⁿ: a) ψ(x) = A e

(ikx)

b) ψ(x,t) = (2/πa²)

1/

e

(i(k₀x - ωt))

e

(- (x - Vgt)² / (a² + 2itħ/m))

where k₀ = Central wave number, Vg = t k₀/m = group velocity, a is width of packet.

Question Bank – Unit-II

Short Questions

  1. Explain the physical significance of the wave function Ψ.
  2. What do you understand by the term’s operator & observables?
  3. Explain the concept of eigenvalues & eigenfunctions.
  4. Write a short note on orthogonality of wave functions.
  5. Discuss the stationary states.
  6. Define the expectation value of a dynamical quantity.

Long Questions

  1. Derive an expression for time-independent & time-dependent Schrödinger equation for a

particle or matter waves.

Or

Derive the time-dependent Schrödinger equation for a free particle in 1-D.

Or

Derive the time-independent Schrödinger wave equation.

  1. Solve the Schrödinger equation for a free particle in a 1-D box. Solve it to get

eigenfunctions.

  1. Discuss the commutation relation for position, momentum, and Hamiltonian operator.
  2. Numericals(Using operators): Prove that

[𝑥

] =iℏ , [𝑥

] =0 , [𝑦

] =0 , [𝑥

] =0 , [𝑦

] =iℏ, [𝑧

] = 0

  1. Check whether the following sets of vectors are linearly dependent or

independent:

(a) A = (2,3,-1), B = (0,1,2), C = (0,0,-5)

(b) A = (3,0,0), B = (0,-2,0), C = (0,0,-1)

  1. Normalize the following quantum states:

(a) |ψ> =

(b) |ψ> =

1

√ 2

|u1> +

1

2

|u2>

(c) |ψ> =

  1. Consider the following two kets:

|ψ> =

|ϕ> =

(a) Find |ψ >

, |ψ>, |ϕ>, |ϕ >

(b) Are |ψ> and |ϕ> orthogonal?

(c) Is |ϕ> normalized? If not, normalize it.

  1. Consider the states:

|ψ> =3 |ϕ 1 > - 7 |ϕ 2 >

|ℵ> =-|ϕ 1 > + 2i|ϕ 2 >

|ϕ1> and |ϕ 2 > are orthonormal.

Calculate |𝜑 + ℵ > 𝑎𝑛𝑑 |ℵ + 𝜑 >

  1. Consider the ket state: |ϕ> =

Find the bra <ϕ | and evaluate the scalar product <ϕ | ψ> if |ψ> =

−3i

2 + i