Verify the correctness of the equation wavelength = h/mv.

Leonard Valentine

Leonard Valentine

Answered question

2022-12-18

Verify the correctness of the equation wavelength = h/mv.

Answer & Explanation

anagenezatmy

anagenezatmy

Beginner2022-12-19Added 4 answers

Wavelength = h/mv
λ = һ/mv
Where:
h = Planck's constant
m = mass
v = Velocity
λ = wavelength
To verify the equation (De Broglie's equation) is dimensionally consistent we use square brackets to mean "the dimensions of" where L, M, T are fundamental quantities of lenght, mass and time respectively.
Hence,
[wavelength ( λ)] = [L]
[h] = [angular momentum] = [L][linear momentum] = [L][M][velocity] =[L][M][L/T]
[v]=[L/T]
Now, we have
[L] = [L][M][velocity] / ( [M][velocity] )
which simplifies to [L] = [L]
which means the equation is dimensionally correct (consistent).

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