Question

The energy difference and the wavelength of light emitted when the electron in a hydrogen atom undergoes transition from the energy level n = 4 to the energy level n =3, given that value of Rydberg constant is 1.0974 $\times$ 10${}^{-7}$ m${}^{-1}$ will be:

• A. $\Delta$E=2.12 $\times {10}^{-19}$ , $\lambda$=1.875 $\times$ 10${}^{-12}$ m
• B. $\Delta$E=1.06 $\times {10}^{-19}$ ,$\lambda$=1.875 $\times$ 10${}^{-12}$ m
• C. $\Delta$E=2.12 $\times {10}^{-19}$ ,$\lambda$=1.875 $\times$ 10${}^{-6}$ m
• D. $\Delta$E=1.06 $\times {10}^{-19}$ ,$\lambda$=1.875 $\times$ 10${}^{-6}$ m

Answer 1

The correct option is D $\Delta$E=1.06 $\times {10}^{-19}$ ,$\lambda$=1.875 $\times$ 10${}^{-6}$ m

As we know,
$1/\lambda =R(1/n_1^2-1/n_2^2)$
$=R(1/3^2-1/4^2)$
$\lambda$=1.875 $\times {10}^{-6}m$
$\Delta E=hc/\lambda$ = $1.06\times {10}^{-19}$