Quantum Mechanics Practice Test Quiz

1. Choose the wrong statement about the spin of an electron, according to quantum mechanics.

• Spin is the rotation of an electron about its own axis.
• Spin is a fundamental property of electrons.
• Spin can take any value between -1/2 and +1/2.
• Spin determines the mass of the electron.

2. The Quantum Mechanical Model of the atom was proposed by which scientist?

• Max Planck
• Niels Bohr
• Albert Einstein
• Erwin Schrodinger

3. The wavelength of matter waves depends on which property of the particle?

• Mass
• Momentum
• Charge
• Temperature

4. Assuming the velocity is constant, which particle has the longest wavelength?

• a proton
• a neutron
• an electron
• a positron

5. What does the uncertainty principle state about measurement errors?

• The error in measurement can be ignored in quantum mechanics.
• The error in measurement is due to the wave nature of particles.
• The error in measurement is due to classical mechanics.
• The error in measurement depends solely on instrument calibration.

6. Given the uncertainties in velocity and position, what is the approximate mass of the object?

• neutron
• electron
• photon
• proton

7. State the law of Stefan-Boltzmann in terms of radiant energy and temperature.

• The radiant energy (E) of a body is directly proportional to the fourth power of its temperature (T). E ∝ T^4.
• The radiant energy (E) of a body is inversely proportional to the square of its temperature (T).
• The total energy emitted by a black body increases linearly with temperature (T).
• The radiant energy (E) decreases as the temperature (T) increases.

8. What are the primary uses of an electron microscope?

• To measure electrical currents in circuits.
• To amplify sound waves for better hearing.
• To study the structure of materials at the atomic and subatomic level.
• To analyze the motion of celestial bodies.

9. Explain the difference between classical mechanics and quantum mechanics with an associated equation.

• Classical mechanics is based on particles` discrete energy states, while quantum mechanics describes continuous energy.
• Classical mechanics deals with non-discrete energy levels, while quantum mechanics does not have energy quantization.
• According to classical mechanics, the radiant energy produced by oscillating objects is continuous. According to quantum mechanics, their energy can be thought of as existing in discrete levels. E = hν.
• In classical mechanics, particles can only have fixed energy values, whereas quantum mechanics allows for any energy.

10. What does Heisenberg’s uncertainty principle imply about position and momentum?

• The position of a particle can be determined without affecting its momentum.
• The position and momentum of a particle cannot both be precisely measured at the same time.
• The position and momentum can be simultaneously determined with high accuracy.
• Heisenberg`s principle states that energy can be measured exactly along with momentum.

11. Who derived the equation of motion for matter-waves?

• Pauli
• Heisenberg
• de-Broglie
• Einstein

12. What happens to the de-Broglie wavelength if the momentum is quadrupled?

• The de-Broglie wavelength is reduced to one-fourth.
• The de-Broglie wavelength becomes quadrupled.
• The de-Broglie wavelength remains the same.
• The de-Broglie wavelength is halved.

13. Calculate the wavelength of light with an energy of 5.22 × 10 –19 J using the appropriate formula.

• 1.20 × 10 –6 m
• 4.76 × 10 –7 m
• 3.81 × 10 –7 m
• 2.96 × 10 –7 m

14. Identify the quantum number not associated with the Schrodinger equation.

• Principal quantum number.
• Spin quantum number.
• Magnetic quantum number.
• Azimuthal quantum number.

15. How many subshells and orbitals are in the principal shell with n = 4?

• 4 subshells (s, p, d, f) and 16 orbitals.
• 3 subshells (s, p, d) and 9 orbitals.
• 2 subshells (s, p) and 4 orbitals.
• 5 subshells (s, p, d, f, g) and 25 orbitals.

16. What is the expected value of the position of a particle in a one-dimensional infinite well?

• x remains constant at zero over time.
• x equals the width of the box divided by 2.
• x is always located at the center of the box.
• x is not fixed over time and switches between the left and right sides of the box.

17. What is the expected value of the energy of a particle in a one-dimensional infinite well?

• H = (1/2)h^2π^2/(ma^2)
• H = (5/3)(h^2π^2/(2ma^2))
• H = 0
• H = h^2/(4ma^2)

18. Which statement is TRUE for the operator ˆA = (1 1 −i 1 + i 0)?

• All statements are true.
• Statement I only.
• Statement II only.
• Statement III only.

19. Determine the orbital of an electron with given angular momentum values in a hydrogen atom.

• 5d
• 4s
• 3f
• 6p

20. What is the minimum uncertainty in the speed of a grain of sand with precise location measurement?

• 10−7 m/s
• 1.0 m/s
• 10−3 m/s
• 10−5 m/s

21. Identify the false prediction of the Bohr model regarding electron behavior.

• The energy levels are continuous.
• The electron moves in elliptical orbits.
• The orbital angular momentum of the electron around the nucleus is a positive integer multiple of ¯h.
• Electrons can occupy any energy state freely.

22. Write the wavefunction ψn,ℓ,m(r, θ, φ) for a hydrogen atom in specific quantum states.

• ψn,ℓ,m(r, θ, φ) = Rnℓ(r) * Yℓ,m(θ) + φ.
• ψn,ℓ,m(r, θ, φ) = Rnℓ(r) – Yℓ,m(θ, φ).
• ψn,ℓ,m(r, θ, φ) = Rnℓ(r) + Yℓ,m(θ, φ).
• ψn,ℓ,m(r, θ, φ) = Rnℓ(r) * Yℓ,m(θ, φ).

23. Provide the radial probability density for an electron in a hydrogen atom with certain quantum numbers.

• P(r) ∝ |Rnℓ(r)|^2.
• P(r) ∝ r^2.
• P(r) ∝ |Yℓ,m(θ, φ)|^2.
• P(r) ∝ |Ψ(r, θ, φ)|^4.

24. Describe the function |Yℓ,m|² when ℓ is a large integer for a hydrogen atom.

• |Yℓ,m|² only has non-zero values along the equator (θ = π/2).
• |Yℓ,m|² is constant across all angles θ, indicating uniform distribution.
• |Yℓ,m|² decreases to zero as ℓ increases, spreading the density.
• |Yℓ,m|² behaves like (sin θ)^(2ℓ), which concentrates the probability density around θ = π/2.

25. What are the equations in the separation of variables for a particle on a cylinder?

• The two equations are for x and y dependence, respectively.
• The two equations are for z and θ dependence, respectively.
• The two equations are for x and θ dependence, respectively.
• The two equations are for y and z dependence, respectively.

26. Solve for the energy eigenvalues for a particle moving on a cylinder of length a.

• En = n^2 / ℏ
• En = n^2 * a
• En = ℏ * (n / a)
• En = ℏ^2 * (n^2 / a^2)

27. What is the ground state energy for a particle on a cylinder of length a?

• The ground state energy is E = -13.6 eV.
• The ground state energy is E = 1/2 * m * v^2.
• The ground state energy is Enℓ = ℏ^2 * (π^2 / a^2).
• The ground state energy is E = h * f.

28. Identify energy levels on a cylinder that do not exist in a finite segment.

• The lowest energy levels that exist on the cylinder but do not exist in the finite segment are those with negative ℓ values.
• The lowest energy levels that exist on the cylinder but do not exist in the finite segment are those with zero energy values.
• The lowest energy levels that exist on the cylinder but do not exist in the finite segment are those with non-zero n values.
• The lowest energy levels that exist on the cylinder but do not exist in the finite segment are those with non-zero ℓ values.

29. Estimate the energy requirement to explore dimensions smaller than a localized particle.

• The energy needed is around 1/J.
• The energy requirement is about m * a^2 / ℏ.
• The minimum energy is approximately ℏ^2 / (m * a^2 * L^2).
• The minimum energy is equal to m * c^2.

30. What does the analysis in part (b) suggest about kinetic and potential energy for an oscillator?

• The total mechanical energy of the oscillator is conserved, with kinetic and potential energy transforming into each other.
• Potential energy is never converted into kinetic energy during oscillation.
• Kinetic energy remains constant while potential energy varies.
• Both kinetic and potential energy are always zero in an oscillator.