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(C) According to Bohr's theory, the energy of an electron in the $n^{th}$ orbit of a hydrogen-like atom is given by $E_n = -13.6 \frac{Z^2}{n^2} \ eV$

Vedclass · Accepted Answer

$1.9$

Vedclass · Answer

(C) According to Bohr's theory, the energy of an electron in the $n^{th}$ orbit of a hydrogen-like atom is given by $E_n = -13.6 \frac{Z^2}{n^2} \ eV$. The energy required to excite an electron from orbit $n_1$ to $n_2$ is $\Delta E = E_{n_2} - E_{n_1} = 13.6 \ Z^2 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} ight) \ eV$. For a hydrogen atom, $Z = 1$, $n_1 = 2$, and $n_2 = 3$. Substituting these values: $\Delta E = 13.6 	imes 1^2 \left( \frac{1}{2^2} - \frac{1}{3^2} ight) \ eV$ $\Delta E = 13.6 \left( \frac{1}{4} - \frac{1}{9} ight) \ eV$ $\Delta E = 13.6 \left( \frac{9 - 4}{36} ight) \ eV$ $\Delta E = 13.6 	imes \frac{5}{36} \ eV \approx 1.888 \ eV \approx 1.9 \ eV$.

In a hydrogen atom, the minimum energy required to excite an electron from the $2^{nd}$ orbit to the $3^{rd}$ orbit is: (in $eV$)

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