The ratio of ground state energy of $\mathrm{Li}^{2+}, \mathrm{He}^{+}, \mathrm{H}$ is

The ratio of ground state energy of $\mathrm{Li}^{2+}, \mathrm{He}^{+}, \mathrm{H}$ is
  1. $3: 2: 1$
  2. $1: 2: 3$
  3. $9: 4: 1$
  4. $1: 4: 9$

Solution

Ground state energy of hydrogen like atom is $E=-13.6 \times \frac{Z^2}{n^2}$ All are in ground state i.e $\mathrm{n}=1$ $\therefore E \propto Z^2$ $\therefore \quad$ The ratio of ground state energy of $\begin{aligned} & \mathrm{E}_{\mathrm{Li}^{2+}}: \mathrm{E}_{\mathrm{He}^{+}}: \mathrm{E}_{\mathrm{H}}(3)^2:(2)^2:(1)^2 \\ &=9: 4: 1 \end{aligned}$

Asked in: AP EAMCET 2024 (22 May Shift 2)

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