Which of the following transitions in a hydro | vedclass

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(A) The energy of a photon emitted during a transition between two energy levels $n_i$ and $n_f$ is given by $\Delta E = E_{n_i} - E_{n_f} = h
u$,whe

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$n = 2$ to $n = 1$

Vedclass · Answer

(A) The energy of a photon emitted during a transition between two energy levels $n_i$ and $n_f$ is given by $\Delta E = E_{n_i} - E_{n_f} = h
u$,where $
u$ is the frequency of the emitted photon.For emission to occur,the electron must transition from a higher energy level to a lower energy level $(n_i > n_f)$.Among the given options,$n = 2$ to $n = 1$ and $n = 6$ to $n = 2$ are emission transitions.The energy difference for $n = 2$ to $n = 1$ is $\Delta E_{2 	o 1} = E_2 - E_1 = -3.4 	ext{ eV} - (-13.6 	ext{ eV}) = 10.2 	ext{ eV}$.The energy difference for $n = 6$ to $n = 2$ is $\Delta E_{6 	o 2} = E_6 - E_2 = -0.38 	ext{ eV} - (-3.4 	ext{ eV}) = 3.02 	ext{ eV}$.Since $\Delta E_{2 	o 1} > \Delta E_{6 	o 2}$,the frequency $
u = \frac{\Delta E}{h}$ is highest for the transition $n = 2$ to $n = 1$.

Which of the following transitions in a hydrogen atom emits a photon of the highest frequency?

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