Question

Calculate the wavelength in angstrom of the photon that is emitted when an electron in Bohr orbit $n=2$ returns to the orbit $n=1$ in the hydrogen atom. The ionization potential of the ground state of hydrogen atom is $2.17\times {10}^{-11}erg/atom$.

Answer 1

For $H-$ atom,

$\frac{1}{\lambda }=R(\frac{1}{n_1^2}-\frac{1}{n_2^2})$
where R is Rydberg Constant

$\frac{1}{\lambda }=R(1-\frac{1}{4})$

$2=\frac{4}{3R}$

$R=1.0973\times {10}^7{m}^{-1}$

$\Rightarrow \frac{1}{R}=912\mathring{A}$

$2=\frac{4}{3}\times 912$

$2=1216\mathring{A}$