Respuesta :
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:
[tex]E=\frac{-R_y}{n^2}[/tex]
[tex]R_y=2.178\times 10^{-18} J[/tex]
Energy of an electron in n = 2:
[tex]E_2=\frac{-R_y}{2^2}=-\frac{R_y}{4}[/tex]
Energy of an electron in n = 3:
[tex]E_3=\frac{-R_y}{3^2}=-\frac{R_y}{9}[/tex]
Energy difference in between both the shells:
[tex]\Delta E=E_3-E_2[/tex] :
[tex]=-\frac{R_y}{9}-(-\frac{R_y}{4})=\frac{5R_y}{36}[/tex]
[tex]\Delta E=\frac{5R_y}{36} =\frac{5\times 2.178\times 10^{-18} J}{36}[/tex]
[tex]=3.025\times 10^{-19} J[/tex]
[tex]\Delta E=3.025\times 10^{-19} J=\frac{hc}{\lambda}[/tex]
[tex]\lambda =\frac{hc\times 36}{3.025\times 10^{-19} J}[/tex]
=[tex]\frac{6.626\times 10^{-34} J s\times 3\times 10^8 m/s}{3.025\times 10^{-19} J}[/tex]
[tex]\lambda =6.571\times 10^{-7} m=657.1 nm[/tex]
[tex]1 m = 10^9 nm[/tex]
The wavelength of the line in the absorption line spectrum of hydrogen caused by transition is 657.1 nm.
