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(D) The energy of an electron in the $n^{th}$ orbit of a hydrogen-like species is given by $E_n = -13.6 	imes \frac{Z^2}{n^2} \ eV$.For $Z = 5$,the e

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$16.53$

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(D) The energy of an electron in the $n^{th}$ orbit of a hydrogen-like species is given by $E_n = -13.6 	imes \frac{Z^2}{n^2} \ eV$.For $Z = 5$,the energy difference between the $4^{th}$ and $3^{rd}$ orbit is $\Delta E = E_4 - E_3$.$\Delta E = -13.6 	imes Z^2 \left( \frac{1}{4^2} - \frac{1}{3^2} ight) = -13.6 	imes 25 \left( \frac{1}{16} - \frac{1}{9} ight)$.$\Delta E = -13.6 	imes 25 \left( \frac{9 - 16}{144} ight) = -13.6 	imes 25 \left( \frac{-7}{144} ight)$.$\Delta E = 13.6 	imes 25 	imes \frac{7}{144} \approx 16.53 \ eV$.

An electron revolves in an orbit around a stationary nucleus with atomic number $Z = 5$. The energy required to excite the electron from the $3^{rd}$ orbit to the $4^{th}$ orbit is .......... $eV$.

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