Which of the following transitions in hydroge | vedclass

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(A) The energy of a photon emitted during an electronic transition is given by $\Delta E = E_{initial} - E_{final} = h
u$,where $
u$ is the frequenc

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$n = 2$ to $n = 1$

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(A) The energy of a photon emitted during an electronic transition is given by $\Delta E = E_{initial} - E_{final} = h
u$,where $
u$ is the frequency.For emission to occur,the electron must transition from a higher energy level to a lower energy level. Thus,options $(b)$ and $(d)$ are excluded as they represent absorption.Comparing the energy differences for the remaining transitions:For $n = 2$ to $n = 1$: $\Delta E_1 = 13.6 \left( \frac{1}{1^2} - \frac{1}{2^2} ight) = 13.6 \left( 1 - 0.25 ight) = 13.6 	imes 0.75 = 10.2 	ext{ eV}$.For $n = 6$ to $n = 2$: $\Delta E_2 = 13.6 \left( \frac{1}{2^2} - \frac{1}{6^2} ight) = 13.6 \left( 0.25 - 0.0277 ight) = 13.6 	imes 0.2223 \approx 3.02 	ext{ eV}$.Since $
u = \frac{\Delta E}{h}$,the transition with the largest energy difference will emit the photon with the highest frequency.Comparing $\Delta E_1$ and $\Delta E_2$,we see that $\Delta E_1 > \Delta E_2$.Therefore,the transition from $n = 2$ to $n = 1$ emits the photon of the highest frequency.

Which of the following transitions in hydrogen atoms emit photons of highest frequency?

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