Q1 / 160 · TS EAMCET 2023 (14 May Shift 1) · Chemistry

The energy of second orbit of hydrogen atom is $-5.45 \times$ $10^{-19} \mathrm{~J}$. What is the energy of first orbit of $\mathrm{Li}^{2+}$ ion (in $\mathrm{J}$ )?

  • A
    $-1.962 \times 10^{-18}$
  • Correct answer
    B
    $-1.962 \times 10^{-17}$
  • C
    $-3.924 \times 10^{-17}$
  • D
    $-3.924 \times 10^{-18}$

Solution

$E_n=-13.6\left[\frac{z^2}{n^2}\right] e V$ $\begin{aligned} & \Rightarrow \mathrm{E}_1=-13.6\left[\frac{3^2}{1^2}\right] \mathrm{eV} \\ & =-122.4 \mathrm{eV} \\ & =-122.4 \times 1.602 \times 10^{-19} \mathrm{~J} \\ & =-1.962 \times 10^{-17} \mathrm{~J}\end{aligned}$

Hence, the correct answer is option: 'B'.

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