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If radius of second Bohr orbit of the $He^+$ ion is 105.8 pm, what is the radius of third Bohr orbit of $Li^{2+}$ ion?
A
158.7 Å
B
158.7 pm
C
15.87 pm
D
1.587 pm
Detailed Solution
From Bohr's model, $r \propto \frac{n^2}{Z}$
$\frac{(r_3)_{Li^{2+}}}{(r_2)_{He^+}} = \frac{n_1^2}{n_2^2} \times \frac{Z_2}{Z_1} = \frac{3 \times 3}{2 \times 2} \times \frac{2}{3}$
$(r_3)_{Li^{2+}} = 105.8 \times \frac{3}{2} = 158.7$ pm