The energy associated with the electron in th | vedclass

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(D) The energy of an electron in the $n^{th}$ orbit is given by $E_n = \frac{E_1}{n^2}$, where $E_1 = -2.18 	imes 10^{-18} \ J$.For the fifth orbit $

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$3.17 	imes 10^{15}$

Vedclass · Answer

(D) The energy of an electron in the $n^{th}$ orbit is given by $E_n = \frac{E_1}{n^2}$, where $E_1 = -2.18 	imes 10^{-18} \ J$.For the fifth orbit $(n = 5)$, $E_5 = \frac{-2.18 	imes 10^{-18}}{5^2} = \frac{-2.18 	imes 10^{-18}}{25} = -0.0872 	imes 10^{-18} \ J$.The energy difference required for excitation is $\Delta E = E_5 - E_1 = (-0.0872 	imes 10^{-18}) - (-2.18 	imes 10^{-18}) = 2.0928 	imes 10^{-18} \ J$.Using the relation $\Delta E = h 
u$, the frequency $
u$ is $
u = \frac{\Delta E}{h} = \frac{2.0928 	imes 10^{-18}}{6.6 	imes 10^{-34}} \approx 3.17 	imes 10^{15} \ Hz$.

The energy associated with the electron in the first orbit of a hydrogen atom is $-2.18 \times 10^{-18} \ J$. The frequency of the light required (in $Hz$) to excite the electron to the fifth orbit is $(h = 6.6 \times 10^{-34} \ Js)$

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