(C) The energy of an electron in the $n^{th}$ orbit of a hydrogen-like species is given by $E_n = -13.6 \times \frac{Z^2}{n^2} \ eV$ or $E_n \propto Z

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(C) The energy of an electron in the $n^{th}$ orbit of a hydrogen-like species is given by $E_n = -13.6 \times \frac{Z^2}{n^2} \ eV$ or $E_n \propto Z^2$. For $He^{+}$,$Z = 2$ and $n = 1$. $E_{He^+} = k \times (2)^2 = 4k = -871.6 \times 10^{-20} \ J$. For $H$,$Z = 1$ and $n = 1$. $E_H = k \times (1)^2 = k$. Therefore,$E_H = \frac{E_{He^+}}{4} = \frac{-871.6 \times 10^{-20}}{4} \ J = -217.9 \times 10^{-20} \ J$.

Class 11 Chemistry Structure of Atom Atomic models and Planck's quantum theory

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The energy of an electron in the first orbit of $He^{+}$ is $-871.6 \times 10^{-20} \ J$. What will be the energy of an electron in the first orbit of hydrogen?

A
$-871.6 \times 10^{-20} \ J$
B
$-435.8 \times 10^{-20} \ J$
C
$-217.9 \times 10^{-20} \ J$
D
$-108.9 \times 10^{-20} \ J$

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The energy of an electron in the first orbit of $He^{+}$ is $-871.6 \times 10^{-20} \ J$. What will be the energy of an electron in the first orbit of hydrogen?

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State the uses of atomic spectra.

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