Which of the following represents the wavelen | vedclass

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(A) The Rydberg formula for hydrogen-like species is given by: $\frac{1}{\lambda} = R Z^2 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)$.For the $H

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$\frac{n^2}{R(n^2-4)}$

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(A) The Rydberg formula for hydrogen-like species is given by: $\frac{1}{\lambda} = R Z^2 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)$.For the $He^{+}$ ion,the atomic number $Z = 2$.For the Balmer series,the transition ends at $n_1 = 2$,and $n_2 = n$ (where $n > 2$).Substituting these values into the formula:$\frac{1}{\lambda} = R (2)^2 \left( \frac{1}{2^2} - \frac{1}{n^2} \right)$$\frac{1}{\lambda} = 4R \left( \frac{1}{4} - \frac{1}{n^2} \right)$$\frac{1}{\lambda} = 4R \left( \frac{n^2 - 4}{4n^2} \right)$$\frac{1}{\lambda} = \frac{R(n^2 - 4)}{n^2}$Therefore,the wavelength $\lambda$ is given by: $\lambda = \frac{n^2}{R(n^2 - 4)}$ or $\lambda = \frac{n^2}{R(n-2)(n+2)}$.

Which of the following represents the wavelength of a spectral line of the Balmer series of the $He^{+}$ ion? ($R=$ Rydberg constant,$n > 2$)

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