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(C) To observe any line of the Balmer series, the hydrogen atom must be excited to at least the $n = 3$ energy level, as the first line of the Balmer

Vedclass · Accepted Answer

$121$

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(C) To observe any line of the Balmer series, the hydrogen atom must be excited to at least the $n = 3$ energy level, as the first line of the Balmer series corresponds to the transition from $n = 3$ to $n = 2$.The energy required to excite an electron from the ground state $(n = 1)$ to the $n = 3$ state is given by:$\Delta E = E_3 - E_1 = 13.6 \left( 1 - \frac{1}{3^2} ight) \,eV$$\Delta E = 13.6 \left( 1 - \frac{1}{9} ight) \,eV = 13.6 	imes \frac{8}{9} \,eV$$\Delta E = 12.088... \,eV \approx 12.09 \,eV$Since the energy of the bombarding electron is $eV$, the potential difference $V$ required is $12.09 \,V$.Given that the potential difference is $\frac{\alpha}{10} \,V$, we have:$\frac{\alpha}{10} = 12.1$$\alpha = 121$.

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