1Which of these has the same dimensions as de Broglie wavelength?
de Broglie wavelength and focal length both have the dimensions [L].
Modern physicsClass 12, Dual Nature of Radiation and Matter
Dimensional formula of de Broglie wavelength
[L]
λ = h/mv. A famous exam check: h over momentum comes out as a length.
How to get the dimensional formula of de Broglie wavelength
- Start from the definition: de Broglie wavelength = plancks constant / momentum.
- 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].
- momentum = mass × velocity, so momentum is [M] × [L T-1] = [M L T-1].
- Put in the dimension of each part: [M L2 T-1] / [M L T-1].
- Add the powers of each base quantity: [L].
Quantities with the dimensions [L]
- Length
- Displacement
- Radius of gyration
- Mean free path
- Wavelength
- Amplitude
- Focal length
- Fringe width
- Bohr radius
Equal dimensions do not make them the same quantity. Compare de Broglie wavelength with the others in the full grid.
Three questions on de Broglie wavelength
2What is the SI unit of de Broglie wavelength?
The SI unit of de Broglie wavelength is the metre (m).
3Which one has different dimensions from the others?
Binding energy is [M L² T⁻²]. The other three are all [L].
de Broglie wavelength: quick answers
What is the dimensional formula of de Broglie wavelength?
The dimensional formula of de Broglie wavelength is [L]. It comes from de Broglie wavelength = plancks constant / momentum.
What is the SI unit of de Broglie wavelength?
The SI unit of de Broglie wavelength is the metre (m).
Which quantities have the same dimensions as de Broglie wavelength?
de Broglie wavelength shares [L] with length, displacement, radius of gyration, mean free path, wavelength, amplitude, focal length, fringe width. Equal dimensions do not make them the same quantity.