NEET 2022 — Chemistry solution

NEET2022Chemistry

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
15.87 pm
B
1.587 pm
C
158.7 Å
D
158.7 pm

Solution

According to the Bohr model, the radius of the n-th orbit of a hydrogen-like species scales as $r \propto \frac{n ^{2}}{Z}$ .

Taking the ratio of (Li $^{2 +}$ , $n = 3$ , $Z = 3$ ) to (He $^{+}$ , $n = 2$ , $Z = 2$ ):

$\frac{r _{3} ( Li ^{2 +} )}{r _{2} ( He ^{+} )} = \frac{n _{1}^{2}}{n _{2}^{2}} \cdot \frac{Z _{2}}{Z _{1}} = \frac{9}{4} \cdot \frac{2}{3} = \frac{3}{2}$ .

$r_{3} (Li^{2 +}) = \frac{3}{2} \times 105.8 = 158.7$ pm.

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