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Nuclear and quantum physics · Question 10

Nuclear and quantum physics · Original GioPhysics question with a detailed, mark-by-mark answer guide.

Demand
discriminating
Marks
13
Topics
1
Answer
Complete
Light falling on a caesium surface, with a photoelectron leaving itlight of wavelength 420 nmcaesium surfacework function 2.1 eVphotoelectron
Fig. 10.1Three parallel rays of light of wavelength 420 nm slant down to the right and meet the flat upper face of a block labelled as a caesium surface with a work function of 2.1 eV. From a point on that same face, further to the right of where the light lands, a single arrow slants up and to the right, marking one photoelectron leaving the metal.
structured13 marks

In a photoelectric experiment, light of wavelength 420 nm is incident on a caesium surface of work function 2.1 eV. Planck's constant is 6.63 × 10⁻³⁴ J s and hc may be taken as 1240 eV nm.

  1. (a)

    Determine Determine the maximum kinetic energy of the emitted photoelectrons, in electronvolts.

    3 marks
  2. (b)

    Determine Determine the threshold wavelength for caesium.

    2 marks
  3. (c)

    Determine Determine the de Broglie wavelength of an electron emitted with the maximum kinetic energy found in (a).

    4 marks
  4. (d)

    Explain Explain how the existence of a threshold frequency, and the absence of any measurable time delay before emission begins even in very dim light, together provide evidence against a purely wave model of light.

    4 marks
Ready to self-mark?Reveal the detailed answer guide
Answer overviewKey answer: photon energy = 1240/420 = 2.95 eV E_k(max) = hf − φ = 2.95 − 2.1 E_k(max) = 0.85 eV
01

(a)

3 marks

Determine Determine the maximum kinetic energy of the emitted photoelectrons, in electronvolts.

How to approach it

List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.

  1. 1

    photon energy = 1240/420 = 2.95 eV

  2. 2

    E_k(max) = hf − φ = 2.95 − 2.1

  3. 3

    E_k(max) = 0.85 eV

02

(b)

2 marks

Determine Determine the threshold wavelength for caesium.

How to approach it

List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.

  1. 1

    at threshold hf = φ, so λ_max = 1240/2.1

  2. 2

    λ_max = 590 nm

03

(c)

4 marks

Determine Determine the de Broglie wavelength of an electron emitted with the maximum kinetic energy found in (a).

How to approach it

List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.

  1. 1

    E_k = 0.85 × 1.60 × 10⁻¹⁹ = 1.36 × 10⁻¹⁹ J

  2. 2

    p = √(2mE_k) = √(2 × 9.11 × 10⁻³¹ × 1.36 × 10⁻¹⁹)

  3. 3

    p = 4.98 × 10⁻²⁵ kg m s⁻¹

  4. 4

    λ = h/p = 6.63 × 10⁻³⁴ / 4.98 × 10⁻²⁵ = 1.3 × 10⁻⁹ m

04

(d)

4 marks

Explain Explain how the existence of a threshold frequency, and the absence of any measurable time delay before emission begins even in very dim light, together provide evidence against a purely wave model of light.

How to approach it

State the outcome first, then link cause to effect with the relevant physical principle. Each link in the reasoning should be explicit enough to earn its own marking point.

  1. 1

    a wave model predicts that energy arrives continuously and spreads over the whole surface, so any frequency should eventually free an electron if the light shines long enough

  2. 2

    instead, no electrons are emitted below the threshold frequency however intense or prolonged the illumination — so the energy must arrive in single indivisible amounts of size hf

  3. 3

    a wave model also predicts a measurable delay in very dim light while an electron accumulates enough energy

  4. 4

    no such delay is observed, because a single photon delivers all of its energy to a single electron in one interaction

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