If radius of second Bohr orbit of the He+\text{He}^+He+ ion is 105.8 pm105.8 \text{ pm}105.8 pm, what is the radius of third Bohr orbit of Li2+\text{Li}^{2+}Li2+ ion?
158.7 pm158.7 \text{ pm}158.7 pm
15.87 pm15.87 \text{ pm}15.87 pm
1.587 pm1.587 \text{ pm}1.587 pm
158.7−158.7^-158.7−
The radius of the nthn^{th}nth Bohr orbit is given by rn=0.529×n2Z A˚=52.9×n2Z pmr_n = 0.529 \times \frac{n^2}{Z} \text{ \AA} = 52.9 \times \frac{n^2}{Z} \text{ pm}rn=0.529×Zn2 A˚=52.9×Zn2 pm. For He+\text{He}^+He+ (Z=2Z=2Z=2), r2=52.9×222=52.9×2=105.8 pmr_2 = 52.9 \times \frac{2^2}{2} = 52.9 \times 2 = 105.8 \text{ pm}r2=52.9×222=52.9×2=105.8 pm. For Li2+\text{Li}^{2+}Li2+ (Z=3Z=3Z=3), r3=52.9×323=52.9×3=158.7 pmr_3 = 52.9 \times \frac{3^2}{3} = 52.9 \times 3 = 158.7 \text{ pm}r3=52.9×332=52.9×3=158.7 pm.
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