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(D) The energy difference for a hydrogen-like ion is given by the formula: $\Delta E = 13.6 	imes Z^2 	imes (\frac{1}{n_1^2} - \frac{1}{n_2^2}) 	ex

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$1.9$

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(D) The energy difference for a hydrogen-like ion is given by the formula: $\Delta E = 13.6 	imes Z^2 	imes (\frac{1}{n_1^2} - \frac{1}{n_2^2}) 	ext{ eV}$.For $O^{7+}$,the atomic number $Z = 8$. The transition is from $n_1 = 1$ to $n_2 = 2$.$\Delta E = 13.6 	imes 8^2 	imes (\frac{1}{1^2} - \frac{1}{2^2}) = 13.6 	imes 64 	imes (1 - 0.25) = 13.6 	imes 64 	imes 0.75 = 652.8 	ext{ eV}$.Converting energy to Joules: $E = 652.8 	imes 1.602 	imes 10^{-19} 	ext{ J} \approx 1.0458 	imes 10^{-16} 	ext{ J}$.The wavelength $\lambda$ is given by $\lambda = \frac{hc}{E}$.$\lambda = \frac{6.626 	imes 10^{-34} 	imes 3 	imes 10^8}{1.0458 	imes 10^{-16}} \approx 1.9 	imes 10^{-9} 	ext{ m} = 1.9 	ext{ nm}$.

What is the wavelength of light required to raise an electron in the $O^{7+}$ ion from $n=1$ shell to $n=2$ shell in $nm$?

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