Question

What would be the approximate quantum number, n, for a circular orbit of hydrogen, $1\times 10-5$ cm in diameter?

Answer 1

Bhor radius is given as,

$r_n=0.529n^2\times {10}^{-10}$m

given that,diameter $={10}^{-7}m$

Thereforee, radius $={10}^{-7}/2$nm

Using bhor radius equation:

$n^2={10}^{-7}/0.529\times {10}^{-10}=1890.3$

$n=43.47$ which is close to 44.