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(B) The energy of the ground state of a hydrogen atom is $E_1 = -13.6 	ext{ eV}$.The energy required to excite the atom to the $n$-th energy level is

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$3$

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(B) The energy of the ground state of a hydrogen atom is $E_1 = -13.6 	ext{ eV}$.The energy required to excite the atom to the $n$-th energy level is given by $\Delta E = E_n - E_1$, where $E_n = -13.6/n^2 	ext{ eV}$.For $n=2$, $\Delta E = -3.4 - (-13.6) = 10.2 	ext{ eV}$.For $n=3$, $\Delta E = -1.51 - (-13.6) = 12.09 	ext{ eV}$.For $n=4$, $\Delta E = -0.85 - (-13.6) = 12.75 	ext{ eV}$.Since the incident electron beam has an energy of $12.5 	ext{ eV}$, it can provide enough energy to excite the hydrogen atoms to the $n=3$ level $(12.09 	ext{ eV})$, but it does not have enough energy to reach the $n=4$ level $(12.75 	ext{ eV})$.Therefore, the hydrogen atoms will be excited up to the $n=3$ energy level.

$A$ $12.5 \text{ eV}$ electron beam is used to bombard gaseous hydrogen at ground state. The energy level up to which the hydrogen atoms would be excited is:

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