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## Homework Statement

a. The first part of this problem was to derive the escape speed (Vesc) for a star of mass M and radius R.

b. The second part is where I am having trouble. It says to equate the Vesc calculated above and derive a formula for Planck length in terms of c, G, and h_bar.

## Homework Equations

This is from the Heisenberg uncertainty section for position and momentum so:

[tex]\Delta[/tex]X * [tex]\Delta[/tex]P = h_bar/2

E = mc

^{2}

## The Attempt at a Solution

The escape velocity I calculated from part a was Vesc = [tex]\sqrt{2GM/R}[/tex]

Equating Vesc to C gives:

C = [tex]\sqrt{2GM/R}[/tex]

Am I supposed to assume that [tex]\Delta[/tex]p = Mc and solve for [tex]\Delta[/tex]x using the Heisenberg uncertainty principle?

I have tried a couple of different methods and I can't get this to simplify down to the form I need. I am pretty sure this is an easy problem, I just am not seeing the trick.