The energy of an electron in first Bohr orbit of $\mathrm{H}-$ atom is $-13.6 \mathrm{eV}$. The energy value…

The energy of an electron in first Bohr orbit of $\mathrm{H}-$ atom is $-13.6 \mathrm{eV}$. The energy value of electron in the excited state of $\mathrm{Li}^{2+}$ is:
  1. $-27.2 \mathrm{eV}$
  2. $30.6 \mathrm{eV}$
  3. $-30.6 \mathrm{eV}$
  4. $27.2 \mathrm{eV}$

Solution

For $\mathrm{Li}^{2+}$ ion
$\begin{aligned} E &=-13.6 \times \frac{Z^{2}}{n^{2}}=-13.6 \times \frac{(3)^{2}}{(2)^{2}} \\ &=\frac{-13.6 \times 9}{4}=-30.6 \mathrm{eV} \end{aligned}$

Asked in: JEE-TOPICTESTS-CHEMISTRY

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