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Atoms — Physics STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 SciencePhysicsAtoms5 Marks
Question
What is the minimum energy that must be given to a $H$ atom in ground state so that it can emit an $\text{H}_\gamma$ line in Balmer series. If the angular momentum of the system is conserved, what would be the angular momentum of such $\text{H}_\gamma$ photon?
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Answer

$\text{H}_\gamma$ in Balmer series corresponds to transition $n = 5$ to $n = 2.$
So, the electron in ground state $n = 1$ must first be put in state $n = 5.$
Energy required $= E_1 - E_5 = 13.6 - 0.54 = 13.06\ eV$
If angular momentum is conserved, angular momentun of photon $=$ change in angular momentum of electron $= L_5 - L_2 $
$= 5h - 2h $
$= 3 \times 1.06 \times 10^{-34} $
$= 3.18 \times 10^{-34}$
$ = 3.18 \times 10^{-38}kh \ m^2/s.$

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