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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 :

horaciocrotte

Answer:

h/(m*c)

Explanation:

Hi!

Lets denote the units of X as [X]

Since the dimentions of h are:

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

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

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

Also we know that:

[tex][c] = \frac{L}{T}[/tex]

So:

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

Therefore

 h/(mc) has dimentiosn of length

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