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

Answer:

h/(m*c)

Explanation:

Hi!

Lets denote the units of X as [X]

Since the dimentions of h are:

$[h] = \frac{ML^{2}}{T}$

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

$\frac{[h]}{[m]} = \frac{L^{2}}{T}}$

Also we know that:

$[c] = \frac{L}{T}$

So:

$[\frac{h}{mc}] = \frac{L^{2}}{T}}*\frac{T}{L}=L$

Therefore

 h/(mc) has dimentiosn of length