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(D) The energy of a photon emitted during a transition between energy levels $n_i$ and $n_f$ is given by $\Delta E = 13.6 \left( \frac{1}{n_f^2} - \fr

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$3 \rightarrow 1$

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(D) The energy of a photon emitted during a transition between energy levels $n_i$ and $n_f$ is given by $\Delta E = 13.6 \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} ight) 	ext{ eV}$.Frequency $
u$ is related to energy by $
u = \frac{\Delta E}{h}$.Calculating the energy differences for the given transitions:$(a)$ $3 ightarrow 2$: $\Delta E \propto \left( \frac{1}{4} - \frac{1}{9} ight) = \frac{5}{36} \approx 0.138$$(b)$ $4 ightarrow 3$: $\Delta E \propto \left( \frac{1}{9} - \frac{1}{16} ight) = \frac{7}{144} \approx 0.048$$(c)$ $4 ightarrow 2$: $\Delta E \propto \left( \frac{1}{4} - \frac{1}{16} ight) = \frac{3}{16} = 0.1875$$(d)$ $3 ightarrow 1$: $\Delta E \propto \left( \frac{1}{1} - \frac{1}{9} ight) = \frac{8}{9} \approx 0.888$Since the transition $3 ightarrow 1$ has the largest energy difference,it corresponds to the highest frequency.

In the following transitions of a hydrogen atom,which one corresponds to the highest frequency of emitted radiation?

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