In which transition is minimum energy emitted | vedclass

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(D) The energy of a transition in a hydrogen-like atom is given by $\Delta E = 13.6 \ Z^2 (\frac{1}{n_1^2} - \frac{1}{n_2^2}) \ eV$.For a transition $

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$n 	o (n - 1) \ [n \geq 4]$

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(D) The energy of a transition in a hydrogen-like atom is given by $\Delta E = 13.6 \ Z^2 (\frac{1}{n_1^2} - \frac{1}{n_2^2}) \ eV$.For a transition $n_2 	o n_1$,the energy emitted is proportional to $(\frac{1}{n_1^2} - \frac{1}{n_2^2})$.Comparing the options:$(A)$ $\infty 	o 1$: $\Delta E \propto (1 - 0) = 1$$(B)$ $2 	o 1$: $\Delta E \propto (1 - 0.25) = 0.75$$(C)$ $3 	o 2$: $\Delta E \propto (0.25 - 0.111) = 0.139$$(D)$ $n 	o (n - 1)$ for $n \geq 4$: As $n$ increases,the energy gap between consecutive levels decreases. For example,if $n=4$,$4 	o 3$ gives $\Delta E \propto (0.111 - 0.0625) = 0.0485$.Since the energy gap between consecutive energy levels decreases as the principal quantum number $n$ increases,the transition $n 	o (n - 1)$ for large $n$ (where $n \geq 4$) results in the minimum energy emission compared to the other specific transitions listed.

In which transition is minimum energy emitted?

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