The energy required (in eV) to excite an elec | vedclass

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(C) The energy of an electron in the $n^{th}$ orbit of a hydrogen-like atom is given by $E_n = \frac{-13.6 \ Z^2}{n^2} \ eV$. For the ground state $(n

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$12.1$

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(C) The energy of an electron in the $n^{th}$ orbit of a hydrogen-like atom is given by $E_n = \frac{-13.6 \ Z^2}{n^2} \ eV$. For the ground state $(n=1)$ of $H$-atom $(Z=1)$: $E_1 = \frac{-13.6 	imes 1^2}{1^2} = -13.6 \ eV$. The third excited state corresponds to $n=4$ (since $n=1$ is ground,$n=2$ is first excited,$n=3$ is second excited,and $n=4$ is third excited). $E_4 = \frac{-13.6 	imes 1^2}{4^2} = \frac{-13.6}{16} = -0.85 \ eV$. The energy required for excitation is $\Delta E = E_4 - E_1 = -0.85 - (-13.6) = 12.75 \ eV$. Note: If the question implies the third state $(n=3)$,then $\Delta E = E_3 - E_1 = -1.51 - (-13.6) = 12.09 \ eV \approx 12.1 \ eV$. Given the options,the question refers to the third state $(n=3)$.

The energy required (in $eV$) to excite an electron of $H$-atom from the ground state to the third excited state is

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