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(A) The energy difference for an electron transition in a hydrogen atom is given by the Rydberg formula: $\Delta E = 13.6 \ eV 	imes (\frac{1}{n_1^2}

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$n = 1$ to $n = 2$

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(A) The energy difference for an electron transition in a hydrogen atom is given by the Rydberg formula: $\Delta E = 13.6 \ eV 	imes (\frac{1}{n_1^2} - \frac{1}{n_2^2})$.For option $A$ ($n=1$ to $n=2$): $\Delta E = 13.6 	imes (1 - 0.25) = 10.2 \ eV$.For option $B$ ($n=2$ to $n=3$): $\Delta E = 13.6 	imes (0.25 - 0.111) \approx 1.89 \ eV$.For option $C$ ($n=2$ to $n=1$): This is an emission process (energy released),not absorption.For option $D$ ($n=3$ to $n=5$): $\Delta E = 13.6 	imes (0.111 - 0.04) \approx 0.96 \ eV$.Comparing the magnitudes of energy required for absorption,the transition from $n=1$ to $n=2$ requires the highest energy.

Which of the following electron transitions in a hydrogen atom requires the highest energy?

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