Quantum Physics (HL)

00:00 10 marks

(a) Explain the concept of quantization of angular momentum in the Bohr model for hydrogen.
[2]
(b) An electron in a hydrogen atom makes a transition from the *n* = 4 energy level to the *n* = 2 energy level.
(i) Calculate the energy of the photon emitted during this transition.
[2]
(ii) Determine the frequency of the emitted photon.
[1]
(c) Outline the experimental evidence that supports the quantization of energy levels in atoms.
[2]
(d) Describe the phenomenon of Compton scattering and explain how it provides evidence for the particle nature of light.
[3]

Part a

3 minutes 2 marks

Question

Explain the concept of quantization of angular momentum in the Bohr model for hydrogen.
[2]

Hint Hint

Hint

Recall Bohr’s specific postulate about which orbits are allowed based on angular momentum.

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Complete Answer

Bohr proposed that the angular momentum (L) of an electron orbiting the nucleus is quantized, meaning it can only take discrete values: \(L = n(h/2π)\), where n is an integer (principal quantum number) and h is Planck’s constant.

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Part b

4 minutes 3 marks

Question

An electron in a hydrogen atom makes a transition from the *n* = 4 energy level to the *n* = 2 energy level.
(i) Calculate the energy of the photon emitted during this transition.
[2]
(ii) Determine the frequency of the emitted photon.
[1]

Hint Hint

Hint

Use the formula \(E_n = -13.6 / n^2\) eV to find the energies. The photon energy is the difference. Then use \(E = hf\). Remember to convert eV to Joules if using \(h\) in J s.

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Complete Answer

(i) Photon energy = 2.55 eV (or \(4.08 \times 10^{-19}\) J).
(ii) Photon frequency = \(6.15 \times 10^{14}\) Hz.

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Part c

3 minutes 2 marks

Question

Outline the experimental evidence that supports the quantization of energy levels in atoms.
[2]

Hint Hint

Hint

Think about the light emitted or absorbed by atoms.

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Complete Answer

Discrete emission spectra (specific frequencies emitted by excited atoms) and discrete absorption spectra (specific frequencies absorbed from continuous light passing through atoms) show that atoms only interact with photons of specific energies, corresponding to the differences between discrete, quantized energy levels.

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Part d

5 minutes 3 marks

Question

Describe the phenomenon of Compton scattering and explain how it provides evidence for the particle nature of light.
[3]

Hint Hint

Hint

Consider the interaction as a collision between a photon and an electron. What quantities are conserved? How does this differ from wave predictions?

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Complete Answer

Compton scattering is the scattering of a high-energy photon (e.g., X-ray) by a charged particle, usually an electron. The scattered photon has a longer wavelength (lower energy) than the incident photon, with the change in wavelength depending on the scattering angle. This observation cannot be explained by classical wave theory but is explained by treating the photon as a particle with momentum \(p = h/\lambda\) colliding with the electron, conserving both energy and momentum in the collision. This particle-collision model successfully predicts the wavelength shift, thus supporting the particle nature of light.

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