1Which of these has the same dimensions as photon energy?
Photon energy and torque both have the dimensions [M L² T⁻²].
Modern physicsClass 12, Dual Nature of Radiation and Matter
Dimensional formula of Photon energy
[M L2 T-2]
E = hν. Planck's constant has the dimension of energy times time, so the frequency cancels the time.
How to get the dimensional formula of photon energy
- Start from the definition: photon energy = plancks constant × frequency.
- velocity = length / time, so velocity is [L] / [T] = [L T-1].
- energy = mass × velocity2, so energy is [M] × [L T-1]2 = [M L2 T-2].
- Planck's constant = energy × time, so Planck's constant is [M L2 T-2] × [T] = [M L2 T-1].
- frequency = 1 / time, so frequency is 1 / [T] = [T-1].
- Put in the dimension of each part: [M L2 T-1] × [T-1].
- Add the powers of each base quantity: [M L2 T-2].
Quantities with the dimensions [M L² T⁻²]
- Work
- Energy
- Kinetic energy
- Potential energy
- Torque
- Torsional constant
- Gravitational potential energy
- Strain energy
- Heat
- Internal energy
- Electric potential energy
- Work function
- Binding energy
Equal dimensions do not make them the same quantity. Compare photon energy with the others in the full grid.
Three questions on photon energy
2What is the SI unit of photon energy?
The SI unit of photon energy is the joule (J).
3Which one has different dimensions from the others?
de Broglie wavelength is [L]. The other three are all [M L² T⁻²].
An equation that uses photon energy
Equation checker
Matching dimensions are necessary, not sufficient. A check cannot see pure numbers such as 1/2 or 2π, so a consistent equation can still be wrong.
Read as
E = h νE[M L2 T-2]=h nu[M L2 T-2]Dimensionally consistentEvery term is [M L2 T-2]
Photon energy: quick answers
What is the dimensional formula of photon energy?
The dimensional formula of photon energy is [M L² T⁻²]. It comes from photon energy = plancks constant × frequency.
What is the SI unit of photon energy?
The SI unit of photon energy is the joule (J).
Which quantities have the same dimensions as photon energy?
Photon energy shares [M L² T⁻²] with work, energy, kinetic energy, potential energy, torque, torsional constant, gravitational potential energy, strain energy. Equal dimensions do not make them the same quantity.