If radius of second Bohr orbit of the H e + ion is 105.8 pm, what is the radius of third Bohr orbit of L i 2 + ion? [2022]

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Solution

Q.
If radius of second Bohr orbit of the $H e^{+}$ ion is 105.8 pm, what is the radius of third Bohr orbit of $L i^{2 +}$ ion [2022]

1 158.7 pm

2 15.87 pm

3 1.587 pm

4 158.7 $Å$

Ans.
(1)

Radius $= r_{0} \times \frac{n^{2}}{Z}$

For $H e^{+}, n = 2, Z = 2$

$r_{{He}^{+}} = r_{0} \times \frac{2 \times 2}{2}; 105.8 = r_{0} \times 2$

$r_{0} = \frac{105.8}{2} pm$

For $L i^{2 +}; n = 3, Z = 3$

$r_{{Li}^{2 +}} = r_{0} \times \frac{{(3)}^{2}}{3} = \frac{105.8}{2} \times 3 = 158.7 pm or 1.587$ $Å$

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