Question

In quantum mechanics, the fundamental constant called Planck's constant, h, has dimensions of [ML^2T^-1 ]. Construct a quantity with the dimensions of length using h, a mass m, and c, the speed of light.

Answer 1

h/(m*c)

Step-by-step explanation:

Hi!

Lets denote the units of X as [X]

Since the dimentions of h are:

`[h] = (ML^(2))/(T)`

If we divide [h] by the units of mass, we get:

`([h])/([m]) = (L^(2))/(T)}`

Also we know that:

`[c] = (L)/(T)`

So:

`[(h)/(mc)] = (L^(2))/(T)}*(T)/(L)=L`

Therefore

h/(mc) has dimentiosn of length