The energy of an electron in the n^{th} orbit | vedclass

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(A) The energy of an electron in the $n^{th}$ orbit is $E_n = -\frac{13.6}{n^2} \, eV$.To move an electron from $n_1 = 2$ to $n_2 = 3$,the required en

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$1.9$

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(A) The energy of an electron in the $n^{th}$ orbit is $E_n = -\frac{13.6}{n^2} \, eV$.To move an electron from $n_1 = 2$ to $n_2 = 3$,the required energy $\Delta E$ is given by:$\Delta E = E_3 - E_2$$\Delta E = \left( -\frac{13.6}{3^2} ight) - \left( -\frac{13.6}{2^2} ight)$$\Delta E = 13.6 \left( \frac{1}{2^2} - \frac{1}{3^2} ight)$$\Delta E = 13.6 \left( \frac{1}{4} - \frac{1}{9} ight)$$\Delta E = 13.6 \left( \frac{9 - 4}{36} ight) = 13.6 	imes \frac{5}{36}$$\Delta E \approx 1.888 \, eV \approx 1.9 \, eV$.

The energy of an electron in the $n^{th}$ orbit of a hydrogen atom is given by $E_n = -\frac{13.6}{n^2} \, eV$. How much energy in $eV$ is required to move an electron from the $n = 2$ orbit to the $n = 3$ orbit?

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