Which energy level transition among the follo | vedclass

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(C) According to the energy relation,$E = \frac{hc}{\lambda}$,which implies $E \propto \frac{1}{\lambda}$.Since the energy of the emitted photon is in

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$n_4 \longrightarrow n_1$

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(C) According to the energy relation,$E = \frac{hc}{\lambda}$,which implies $E \propto \frac{1}{\lambda}$.Since the energy of the emitted photon is inversely proportional to its wavelength,the transition with the largest energy difference will result in the shortest (least) wavelength.The energy difference $\Delta E$ is given by $\Delta E = 13.6 	imes Z^2 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} ight) 	ext{ eV}$.Comparing the transitions:$(A)$ $n_4 \longrightarrow n_3$: $\Delta E \propto (\frac{1}{9} - \frac{1}{16}) = \frac{7}{144} \approx 0.048$$(B)$ $n_4 \longrightarrow n_2$: $\Delta E \propto (\frac{1}{4} - \frac{1}{16}) = \frac{3}{16} = 0.1875$$(C)$ $n_4 \longrightarrow n_1$: $\Delta E \propto (\frac{1}{1} - \frac{1}{16}) = \frac{15}{16} = 0.9375$$(D)$ $n_2 \longrightarrow n_1$: $\Delta E \propto (\frac{1}{1} - \frac{1}{4}) = \frac{3}{4} = 0.75$The transition $n_4 \longrightarrow n_1$ has the largest energy difference,therefore it corresponds to the least wavelength.

Which energy level transition among the following will have the least wavelength?

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