Question

calculate the energy and frequency of light required to excite an electron in hydrogen atom from first energy level to fourth energy level

Answer 1

According to Rydberg equation,
$\frac{1}{\lambda }$ = R ( $\frac{1}{{n_1}^2}-\frac{1}{{n_2}^2}$ )

where R = 109677 cm^-1 , n₁ = 1 and n₂ = 4
Substituiting the values.
$\frac{1}{\lambda }$ = 109677 ( $\frac{1}{1^2}-\frac{1}{4^2}$ )
On solving we get,
$\lambda$ = 9725nm
now to calculate frequency:
$\nu =\frac{c}{\lambda }$

where c = 3 $\times$ 10⁸ ms^-1 and $\lambda$ = 9725 $\times$ 10^-9m
$\nu =\frac{3\times {10}^{8}m{s}^{-1}}{9725\times {10}^{-9}m}$
$\nu =3.08\times {10}^{13}{s}^{-1}$

Energy, E = $h\nu$
where h = 6.626 $\times$ 10^-34 Js
E = $6.626\times {10}^{-34}\times 9725\times {10}^{13}$
E = 6.44 $\times$ 10^-13 J