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

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From $n = 1$ to $n = \infty$

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(C) The energy required for an electron transition in a hydrogen atom is given by the Rydberg formula: $\Delta E = 13.6 	imes Z^2 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} ight) 	ext{ eV}$.For a hydrogen atom,$Z = 1$.$(A)$ $n = 1 	o n = 2$: $\Delta E = 13.6 	imes (1 - 1/4) = 10.2 	ext{ eV}$.$(B)$ $n = 2 	o n = 3$: $\Delta E = 13.6 	imes (1/4 - 1/9) \approx 1.89 	ext{ eV}$.$(C)$ $n = 1 	o n = \infty$: $\Delta E = 13.6 	imes (1/1 - 1/\infty) = 13.6 	ext{ eV}$.$(D)$ $n = 3 	o n = 5$: $\Delta E = 13.6 	imes (1/9 - 1/25) \approx 0.97 	ext{ eV}$.Comparing these values,the transition from $n = 1$ to $n = \infty$ requires the largest amount of energy.

Which of the following electron transitions in a hydrogen atom will require the largest amount of energy?

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