Which of the following electronic transitions | vedclass

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(B) The energy difference between two energy levels in a hydrogen atom is given by $\Delta E = 13.6 	imes Z^2 	imes (\frac{1}{n_1^2} - \frac{1}{n_2^

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$n=1$ to $n=2$

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(B) The energy difference between two energy levels in a hydrogen atom is given by $\Delta E = 13.6 	imes Z^2 	imes (\frac{1}{n_1^2} - \frac{1}{n_2^2}) 	ext{ eV}$.For a hydrogen atom $(Z=1)$,the energy difference is $\Delta E = 13.6 	imes (\frac{1}{n_1^2} - \frac{1}{n_2^2}) 	ext{ eV}$.Comparing the transitions:$(A)$ $n=4 ightarrow n=5$: $\Delta E = 13.6 	imes (\frac{1}{16} - \frac{1}{25}) \approx 0.306 	ext{ eV}$.$(B)$ $n=1 ightarrow n=2$: $\Delta E = 13.6 	imes (\frac{1}{1} - \frac{1}{4}) = 13.6 	imes 0.75 = 10.2 	ext{ eV}$.$(C)$ $n=3 ightarrow n=5$: $\Delta E = 13.6 	imes (\frac{1}{9} - \frac{1}{25}) \approx 0.967 	ext{ eV}$.$(D)$ $n=2 ightarrow n=3$: $\Delta E = 13.6 	imes (\frac{1}{4} - \frac{1}{9}) \approx 1.889 	ext{ eV}$.Since the energy gap decreases as the principal quantum number $n$ increases,the transition from the ground state $(n=1)$ to the first excited state $(n=2)$ involves the largest energy change.

Which of the following electronic transitions in a hydrogen atom will require the highest energy?

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