Not given in the exam, recall it.
What it is for
Photon energy (wavelength form) is used in Quantum Physics (SPM Physics Form 5). Keep the SI units in every line of working. Quantum Physics
Symbols and SI units
| Symbol | Meaning | SI unit |
|---|---|---|
| E | photon energy | J |
| h | Planck constant | J s |
| c | speed of light | m s⁻¹ |
| λ | wavelength | m |
Rearrangements
λ = hc / EE λ = hc
Worked example
Common trap
Understanding photon energy (wavelength form)
The equation E = hc / λ gives a photon's energy from its wavelength. Here E is the photon energy in joules (J), h is the Planck constant in joule-seconds (J s), c is the speed of light in metres per second (m s⁻¹), and λ is the wavelength in metres (m).
It comes from combining E = hf with the wave relation c = fλ, so f = c / λ. Because wavelength sits in the denominator, energy and wavelength are inversely related: shorter wavelengths (violet, ultraviolet) carry more energy per photon than longer ones (red, infrared).
Rearrange it as λ = hc / E to find the wavelength from a known energy, or Eλ = hc to compare two photons. Use h = 6.63 × 10⁻³⁴ J s and c = 3.0 × 10⁸ m s⁻¹.
A worked example, step by step
Find the energy of a photon of blue light of wavelength λ = 4.5 × 10⁻⁷ m (450 nm). Take h = 6.63 × 10⁻³⁴ J s and c = 3.0 × 10⁸ m s⁻¹.
Start from the formula:
E = hc / λ
Substitute with units:
E = (6.63 × 10⁻³⁴ J s × 3.0 × 10⁸ m s⁻¹) / (4.5 × 10⁻⁷ m)
Work out the numerator first:
E = (1.989 × 10⁻²⁵) / (4.5 × 10⁻⁷) J
Divide:
E = 4.42 × 10⁻¹⁹ J to three significant figures. The metre units cancel, leaving joules.
Common mistakes and how this is tested
The classic trap is leaving the wavelength in nanometres. Convert first: 1 nm = 10⁻⁹ m, so 450 nm = 4.5 × 10⁻⁷ m.
Forgetting this makes the answer wrong by a factor of a billion.
Further errors to watch:
- Placing λ on top instead of the bottom of the fraction.
- Using c = 3.0 × 10⁶ instead of 3.0 × 10⁸ m s⁻¹.
- Mixing this up with E = hf when only wavelength is given.
Under calculate, show the substitution and the units. Under explain, state that a shorter wavelength gives a higher photon energy because E is inversely proportional to λ.
Source: DSKP KSSM Physics Form 4 and 5 (Versi English), Sijil Pelajaran Malaysia: Format Pentaksiran mulai 2021, Fizik (4531) (Bahagian Pembangunan Kurikulum (BPK), KPM)