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

In summary, the conversation discussed the calculation of the lowest gravitational Bohr radius using the equation F= G Me Mp / r^2 and the given values of physical constants. The suggested approach of setting F equal to 13.6 eV was deemed incorrect. The question of why there is a minimum radius was also raised. However, it was later clarified in class.
  • #1
annorax
2
0

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!
 
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  • #2
annorax said:
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?)
 
  • #3
Actually, he realized that we had not gone over it yet and discussed it in class today. Thanks anyway!
 

1. What is the gravitational Bohr radius?

The gravitational Bohr radius, also known as the Schwarzschild radius, is a measure of the size of the event horizon of a black hole. It is the distance from the center of a black hole at which the escape velocity equals the speed of light.

2. How is the gravitational Bohr radius calculated?

The gravitational Bohr radius is calculated using the mass of the black hole and the gravitational constant. The formula is R = 2GM/c², where R is the radius, G is the gravitational constant, M is the mass of the black hole, and c is the speed of light.

3. What is the significance of the gravitational Bohr radius?

The gravitational Bohr radius is significant because it marks the boundary of the event horizon of a black hole. Anything that passes beyond this radius, including light, is unable to escape the gravitational pull of the black hole.

4. Can the gravitational Bohr radius change?

Yes, the gravitational Bohr radius can change depending on the mass of the black hole. A larger mass will result in a larger radius, while a smaller mass will result in a smaller radius. It is an important factor in understanding the properties and behavior of black holes.

5. How does the gravitational Bohr radius relate to the Bohr model of the atom?

The gravitational Bohr radius is named after the Bohr model of the atom, which describes the structure of an atom with electrons orbiting a nucleus. Similarly, the gravitational Bohr radius describes the size and structure of a black hole, with the event horizon acting as the "nucleus" and objects orbiting around it.

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