What is the lowest gravitational Bohr radius in terms of light years?

[annorax]

Homework Statement

If the attractive forces between an electron and proton only due to gravity is

F=(Gx Me x Mp)/r^2.

What is the lowest gravitational Bohr radius?
c=2.99799 x 10^8 m/s
Me= 9.10939 x 10^-31
Mp=1.67262 x 10^-27
h= 1.05457 x 10^-34
G= 6.67259 x 10^-11 Nm^2/kg^2
R= 1.097373 x 10^7m^-1

Answer in units of lt yr.

Homework Equations

F= G Mp Me / r^2

The Attempt at a Solution

This was not covered in detail in class, just the basics. My idea was to set F equal to 13.6 eV, convert to Joules, and solve the equation for r, which gave me an answer of 2.2831 x 10^-41 lightyears. A nudge in the right direction would be greatly appreciated!

 

[zhermes]

My idea was to set F equal to 13.6 eV

'F' is a force, and 13.6 eV is an energy---i.e. that won't work.

Why is it that there has to be a minimum radius? (i.e. why can't the radius be arbitrarily small?)

 

[annorax]

Actually, he realized that we had not gone over it yet and discussed it in class today. Thanks anyway!