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Question

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


Solution

Wavelength = h/mv
λ = һ/mv 

Where: 
h = Planck's constant 
m = mass 
v = Velocity 
λ = wavelength
To check 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.
Therefore,

[wavelength (λ)] = [L] 
[h] = [angular momentum] = [L][linear momentum] = [L][M][velocity] =[L][M][L/T]
[v]=[L/T]
So we now have 
[L] = [L][M][velocity] / ( [M][velocity] ) 
which simplifies to [L] = [L] 
which means the equation is dimensionally correct (consistent).


Physics

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