Check the dimensional correctness of λ = h/mv
de Broglie wavelength. The wavelength of a particle of mass m moving at speed v.
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.
λ = h / (m v)lambda[L]=h/mv[L]Step by step
1. What each symbol stands for
- λ wavelength [L]
- h Planck's constant [M L2 T-1]
- m mass [M]
- v velocity [L T-1]
2. The dimensions of each term
- lambda [L] [L]
- h/mv [M L2 T-1] / ([M] × [L T-1]) [L]
3. Compare
Every term has dimensions [L], so the equation is dimensionally consistent.
What it proves and what it does not
It can show
- Every term that is added or subtracted has the same dimensions, so the sum makes sense.
- Both sides of the equals sign have the same dimensions.
- Angles inside sin, cos and similar functions are pure numbers.
It cannot show
- A pure number such as 1/2 or 2π has no dimensions, so a check cannot see a missing or wrong one.
- Two quantities with the same dimensions, such as work and torque, cannot be told apart.
- A sign error or a wrong power that keeps the dimensions equal goes unnoticed.
Matching dimensions are necessary but not sufficient. Pure numbers such as 1/2 or 2π have no dimensions, so a check cannot see them, and an equation with matching dimensions can still be wrong.
Look up each quantity
λ = h/mv: quick answers
Is λ = h/mv dimensionally correct?
Yes. Every term has the same dimensions, [L], so λ = h/mv is dimensionally consistent. That does not prove the equation itself is correct.
Does a dimension check prove λ = h/mv is right?
No. A check can show that an equation is wrong, but it cannot show that it is right. Pure numbers such as 1/2 and 2π have no dimensions, so the check cannot see them.