Calculate the radius of first orbit of $\mathrm{Li}^{++}$.

Calculate the radius of first orbit of $\mathrm{Li}^{++}$.
  1. 70.53 pm
  2. $\quad 158.7 \mathrm{pm}$
  3. $\quad 17.63 \mathrm{pm}$
  4. 282.13 pm

Solution

$\mathrm{r}_{\mathrm{n}}=\frac{52.9\left(\mathrm{n}^2\right)}{\mathrm{Z}} \mathrm{pm}$
For $\mathrm{Li}^{++}, \mathrm{Z}=3$ First orbit, n = 1 $\mathrm{r}_{\mathrm{n}}=\frac{52.9\left(\mathrm{n}^2\right)}{\mathrm{Z}} \cdot \mathrm{pm}=\frac{52.9(1)^2}{3}=17.63 \mathrm{pm}$

Asked in: MHT CET 2024 (15 May Shift 1)

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