A sample of hydrogen atoms in its ground stat | vedclass

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(A, B) The energy required for a transition in $He^{+}$ is given by $E = 13.6 	imes Z^2 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} ight)$. For $He^{+

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Smallest wavelength of $He^{+}$ spectrum is obtained when transition takes place from $n=4$ to $n=3$

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(A, B) The energy required for a transition in $He^{+}$ is given by $E = 13.6 	imes Z^2 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} ight)$. For $He^{+}$, $Z=2$, so $E = 13.6 	imes 4 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} ight) = 54.4 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} ight) eV$.For a transition from $n=2$ to $n=4$, $E = 54.4 \left( \frac{1}{4} - \frac{1}{16} ight) = 54.4 \left( \frac{3}{16} ight) = 10.2 eV$.Since the incident photon energy is $10.2 eV$, the $He^{+}$ electron can be excited from $n=2$ to $n=4$.Once in the $n=4$ state, the number of spectral lines emitted is given by $\frac{n(n-1)}{2} = \frac{4(4-1)}{2} = 6$.Therefore, statements $A$ and $B$ are correct.

$A$ sample of hydrogen atoms in its ground state is radiated with photons of $10.2 eV$ energy. The radiation emitted from the sample is absorbed by excited ionized $He^{+}$ ions. Which of the following statement$(s)$ is/are true?

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