Question

what is the minimum energy that must be given to a hydrogen atom in ground state so that it can emit H beta lines in lyman series​

Answer 1

what is the minimum energy that must be given to a hydrogen atom in ground state so that it can emit H beta lines in lyman series.

$H_{\beta}$ is Lyman series corresponds to transition from $n_1$ = 3 to $n_2$= 1

so, amount of energy that must be given to a hydrogen atom in ground state so that it can emits $H_{\beta}$ lines in Lyman series. , E = $13.6\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)$ eV

=$13.6\left(\frac{1}{1}-\frac{1}{3^2}\right)$ eV

= $13.6\times\frac{8}{9}$ eV

=12.088 eV

hence, answer is 12.088 eV

Answer 2

Hγ in Balmer series corresponds to transition n = 5 to n = 2. So the electron in ground state n = 1 must first be put in state n = 5. Energy required = E1 – E5 = 13.6 – 0.54 = 13.06 eV.  If angular momentum is conserved, angular momentum of photon = change in angular momentum of the electron