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9702 · 22.1

Energy and momentum of a photon — practice questions

Practice and worked examples for 9702 Energy and momentum of a photon. Short previews only — attempt the full question in MarkScheme against the official scheme.

Worked example 1

A red laser emits light with a wavelength of 650 nm. Calculate the energy of a single photon from this laser in (i) Joules and (ii) electronvolts. (Planck's constant h = 6.63 × 10⁻³⁴ Js, speed of light c = 3.00 × 10⁸ m s⁻¹)

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  1. Identify knowns: λ = 650 nm = 650 × 10⁻⁹ m h = 6.63 × 10⁻³⁴ Js c = 3.00 × 10⁸ m s⁻¹
  2. (i) Calculate energy in Joules using E = hc/λ: E = (6.63 × 10⁻³⁴ J s × 3.00 × 10⁸ m s⁻¹) / (650 × 10⁻⁹ m) E = (1.989 × 10⁻²⁵) / (6.50 × 10⁻⁷) J E ≈ 3.06 × 10⁻¹⁹ J
  3. (ii) Convert energy to electronvolts: 1 eV = 1.60 × 10⁻¹⁹ J E (eV) = E (J) / (1.60 × 10⁻¹⁹ J/eV) E (eV) = (3.06 × 10⁻¹⁹ J) / (1.60 × 10⁻¹⁹ J/eV) E (eV) ≈ 1.91 eV

Worked example 2

A monochromatic blue light source has a power output of 2.5 mW and emits light of wavelength 450 nm. Calculate: (i) the energy of a single photon in Joules, (ii) the number of photons emitted per second, and (iii) the momentum of a single photon. (h = 6.63 × 10⁻³⁴ Js, c = 3.00 × 10⁸ m s⁻¹)

Show solution outline
  1. Identify knowns and convert units: Power, P = 2.5 mW = 2.5 × 10⁻³ J s⁻¹ Wavelength, λ = 450 nm = 450 × 10⁻⁹ m
  2. (i) Calculate the energy of a single photon (E): Use the formula E = hc/λ E = (6.63 × 10⁻³⁴ J s × 3.00 × 10⁸ m s⁻¹) / (450 × 10⁻⁹ m) E = 1.989 × 10⁻²⁵ / 4.50 × 10⁻⁷ J E ≈ 4.42 × 10⁻¹⁹ J
  3. (ii) Calculate the number of photons per second (N): Power is the total energy per second (P = N × E). N = P / E N = (2.5 × 10⁻³ J s⁻¹) / (4.42 × 10⁻¹⁹ J) N ≈ 5.66 × 10¹⁵ photons s⁻¹
  4. (iii) Calculate the momentum of a single photon (p): Use the formula p = h/λ p = (6.63 × 10⁻³⁴ J s) / (450 × 10⁻⁹ m) p ≈ 1.47 × 10⁻²⁷ kg m s⁻¹
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