# Bohr Radius - what happens when n=100?

1. Mar 9, 2008

### wombat4000

1. The problem statement, all variables and given/known data

i have been given a question that asks to me to calculate the radii of the first, second and third 'permitted' electron orbits in hydrogen. I did this fine by using the Bohr Equation, each time just changing the n value to either 2 or 3 resulting in the first value of the radius being multiplied by 4 or 9.

The next part asks me to calculate the radius when n=100, experience of answering questions makes me think that something different will happen when n is so large and that they are not looking for me to just multiply by 100000. Does anyone know what?

2. Mar 9, 2008

### kdv

When n approaches $$1/\alpha \approx 137$$ the system becomes relativistic so the whole derivation of Bohr energy levels falls apart, one must solve the Dirac equation. But you won't notice this if you only look at the Borh radius.

3. Mar 10, 2008

### pam

For a point proton, the formula for r works for all n.
However for a physical proton of radius~1fm, the Bohr radius becomes so small for large n that the finite size of the proton must be considered.

4. Mar 10, 2008

### kdv

But the value increases with n, it does not decrease.

5. Mar 10, 2008

### pam

I am careless. Thank you.