For a hydrogen atom,which of the following el | vedclass

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(A) The energy change for an electron transition in a hydrogen atom is given by $\Delta E = 13.6 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} ight) 	ex

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

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(A) The energy change for an electron transition in a hydrogen atom is given by $\Delta E = 13.6 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} ight) 	ext{ eV}$.For option $A$: $\Delta E = 13.6 \left( \frac{1}{1^2} - \frac{1}{\infty^2} ight) = 13.6 	ext{ eV}$.For option $B$: $\Delta E = 13.6 \left( \frac{1}{2^2} - \frac{1}{3^2} ight) = 13.6 \left( \frac{1}{4} - \frac{1}{9} ight) = 13.6 \left( \frac{5}{36} ight) \approx 1.89 	ext{ eV}$.For option $C$: $\Delta E = 13.6 \left( \frac{1}{1^2} - \frac{1}{2^2} ight) = 13.6 \left( 1 - 0.25 ight) = 13.6 	imes 0.75 = 10.2 	ext{ eV}$.For option $D$: $\Delta E = 13.6 \left( \frac{1}{3^2} - \frac{1}{5^2} ight) = 13.6 \left( \frac{1}{9} - \frac{1}{25} ight) = 13.6 \left( \frac{16}{225} ight) \approx 0.97 	ext{ eV}$.Comparing the values,the transition from $n = \infty$ to $n = 1$ involves the largest energy change.

For a hydrogen atom,which of the following electron transitions requires the highest energy?

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