Which of the following transitions emits a ph | vedclass

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Question

(D) The frequency of an emitted photon is given by $
u = \frac{\Delta E}{h}$. To maximize frequency,we must maximize the energy difference $\Delta E$

Vedclass · Accepted Answer

First spectral line of the Lyman series

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(D) The frequency of an emitted photon is given by $
u = \frac{\Delta E}{h}$. To maximize frequency,we must maximize the energy difference $\Delta E$ between the energy levels. The energy of a level is given by $E_n = -13.6 \ 	ext{eV} 	imes \frac{Z^2}{n^2}$. The Lyman series involves transitions to $n_1 = 1$. The first line of the Lyman series is $n_2 = 2 	o n_1 = 1$. The energy difference is $\Delta E = 13.6 	imes (1 - \frac{1}{4}) = 13.6 	imes 0.75 = 10.2 \ 	ext{eV}$. Comparing this with other series: Balmer $(n_1 = 2)$: $\Delta E = 13.6 	imes (\frac{1}{4} - \frac{1}{16}) = 13.6 	imes 0.1875 = 2.55 \ 	ext{eV}$. Paschen $(n_1 = 3)$: $\Delta E = 13.6 	imes (\frac{1}{9} - \frac{1}{25}) \approx 0.96 \ 	ext{eV}$. Humphrey $(n_1 = 6)$: $\Delta E$ is even smaller. Thus,the first spectral line of the Lyman series has the largest energy gap and consequently the maximum frequency.

Which of the following transitions emits a photon with the maximum frequency?

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