Answer to Question #204571 in Electricity and Magnetism for Daryll

Question

A particular hydrogen atom is in an energy state with E = –2.418×10^-19 J. Calculate the maximum angular momentum this atom could have.

Give the value as a multiple of ℏ to 2 decimal places. (e.g. if you calculated L = 1.41ℏ, then you would enter "1.41" as your value).

Answer 1

$E=\frac{E_0}{n^2},\implies$

$n=\sqrt{\frac{E_0}{E}}=\sqrt{\frac{13.6}{2.418}}=2.37,$

$L_e=\hbar \sqrt{n(n+1)}=28.26\hbar.$