What is the Wavenumber and Transition for an H-Atom with n=732 to n=731?

[rayman123]

Homework Statement

Calculate a diameter of an H-atom with n=732. Calculate also the value of the wavenumber corresponding to the transition from n=732 to n=731

Homework Equations

$$E_{trans}= \frac{-E_{h}}{(732)^2}-\frac{-E_{h}}{(731)^2}}$$

The Attempt at a Solution

$$E_{trans}= \frac{-13.6}{(732)^2}-\frac{-13.6}{(731)^2}}=6.95\cdot10^{-5} eV$$

$$E=\frac{hc}{\lambda}\Rightarrow \lambda=\frac{hc}{E}=\frac{4.135\cdot10^{-15}\cdot 3\cdot10^8}{6.95\cdot10^{-5}}=0.0178 m$$

Homework Statement

now going back to the wavenumber, i was not sure which formula i should use...
$$k=\frac{2\pi}{\lambda} or \nu=\frac{1}{\lambda}$$
I have chosen the second one and i got
$$\nu=\frac{1}{0.0178}=56.18 m^{-1}$$

Homework Statement

Is that a relevant result?

The Attempt at a Solution

the diameter will be=
$$d_{n}=2\cdot r_{0}\cdot n^2= 2\cdot (732)^2\cdot 5.291\cdot10^{-5} = 5.67\cdot10^{-5} m$$

 

[guerom00]

Seems OK :)