Question

The energy E of the electron in a hydrogen atom can be calculated from the Bohr formula:

Answer 1

Answer:

The wavelength of the line in the absorption line spectrum of hydrogen caused by transition is 657.1 nm.

Explanation:

Energy of the electron in a hydrogen atom in nth shell:

$E=\frac{-R_y}{n^2}$

$R_y=2.178\times 10^{-18} J$

Energy of an electron in n = 2:

$E_2=\frac{-R_y}{2^2}=-\frac{R_y}{4}$

Energy of an electron in n = 3:

$E_3=\frac{-R_y}{3^2}=-\frac{R_y}{9}$

Energy difference in between both the shells:

$\Delta E=E_3-E_2$ :

$=-\frac{R_y}{9}-(-\frac{R_y}{4})=\frac{5R_y}{36}$

$\Delta E=\frac{5R_y}{36} =\frac{5\times 2.178\times 10^{-18} J}{36}$

$=3.025\times 10^{-19} J$

$\Delta E=3.025\times 10^{-19} J=\frac{hc}{\lambda}$

$\lambda =\frac{hc\times 36}{3.025\times 10^{-19} J}$

=$\frac{6.626\times 10^{-34} J s\times 3\times 10^8 m/s}{3.025\times 10^{-19} J}$

$\lambda =6.571\times 10^{-7} m=657.1 nm$

$1 m = 10^9 nm$

The wavelength of the line in the absorption line spectrum of hydrogen caused by transition is 657.1 nm.