Question

1) Determine the wavelength of light emitted when an electron in a hydrogen atom makes a transition from an orbital in n = 6 to an orbital in n = 5.

2) Determine the wavelength of the light absorbed when an electron in a hydrogen atom makes a transition from an orbital in which n = 2 to an orbital in which n =3

Answer 1

Answer (1) (2)

By using Rydberg equation,

$\Delta E = R_{H}[(1/n_{i}^{2})-(1/n_{f}^{2})]$

where R_H = Rydberg Constant 2.18 $\times$ 10^-18 J

n_f = final energy level

n_i = initial energy level

Therefore,

1) transition from n=6 to n=5;

n_f = 5

n_i = 6

$\Delta E =$ 2.18 * $\times$ 10^-18 J [(1/6²) - (1/5²)] = -2.66 * 10^-20 J (-ve Sign represents energy released)

we know,

$\Delta E = hc/\lambda$   

where h= 6.626 $\times$ 10^-34 Js and c= 3 $\times$ 10⁸ m/s

so, $\lambda =$ (6.626 $\times$ 10^-34 Js $\times$ 3 $\times$ 10⁸ m/s) / (2.66 * 10^-20 J) = 7.47 $\times$ 10^-6 m = 7472nm

2) transition from n=2 to n=3;

n_f = 3

n_i = 2

$\Delta E =$ 2.18 * $\times$ 10^-18 J [(1/2²) - (1/3²)] = 3.03 * 10^-19 J

$\lambda =$ (6.626 $\times$ 10^-34 Js $\times$ 3 $\times$ 10⁸ m/s) / (3.03 $\times$ 10^-19 J) = 6.56 $\times$ 10^-7 m = 656nm