Which of the following transitions has the mi | vedclass

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(A) The wavelength $(\lambda)$ of a transition is inversely proportional to the energy difference $(\Delta E)$ between the energy levels,given by the

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$n_4 	o n_1$

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(A) The wavelength $(\lambda)$ of a transition is inversely proportional to the energy difference $(\Delta E)$ between the energy levels,given by the relation $\Delta E = \frac{hc}{\lambda}$.For a hydrogen-like atom,the energy difference is $\Delta E = 13.6 Z^2 (\frac{1}{n_1^2} - \frac{1}{n_2^2}) 	ext{ eV}$.To have the minimum wavelength,the transition must have the maximum energy difference.Comparing the transitions:$(A)$ $n_4 	o n_1$: $\Delta E \propto (1 - \frac{1}{16}) = \frac{15}{16} = 0.9375$$(B)$ $n_2 	o n_1$: $\Delta E \propto (1 - \frac{1}{4}) = \frac{3}{4} = 0.75$$(C)$ $n_4 	o n_2$: $\Delta E \propto (\frac{1}{4} - \frac{1}{16}) = \frac{3}{16} = 0.1875$$(D)$ $n_3 	o n_1$: $\Delta E \propto (1 - \frac{1}{9}) = \frac{8}{9} \approx 0.888$Since the transition $n_4 	o n_1$ has the largest energy difference,it corresponds to the minimum wavelength.

Which of the following transitions has the minimum wavelength?

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