Physics GRE GR 1777

- Quantum Mechanics (Planck length) + Dimensional analysis

Solution 1) If you don’t know the Planck length, that’s fine. This question asks that you know about the dimensional analysis.

The unit of the length should be . To find the proper expression for length, we construct the equation like this:

The dimensions of this equation gives

We can easily calculate their orders.

Therefore, the Planck length is

The answer is (A).

Solution 2) If you already know about the Planck length, then you have nothing to worry about.

The Planck length is

Reference)

https://en.wikipedia.org/wiki/Planck_length