Question

An electron revolves around $L{i}^{+2}$ nucleus at a distance of $1.587A$. The speed of electron should be:

• A. $2.188\times {10}^{6}m/s$
• B. $6.564\times {10}^{6}m/s$
• C. $7.293\times {10}^{5}m/s$
• D. $7.293\times {10}^{6}m/s$

Answer 1

The correct option is A $2.188\times {10}^{6}m/s$

We know that, $\frac{1}{2}{mU}^2=\frac{Z{e}^2}{Zr}$

$\Rightarrow U^2=\frac{{Ze}^2}{m}.\frac{1}{r}=\frac{3\times {(1.602\times {10}^{-19})}^4}{9.1\times {10}^{-31}\times 1.587\times {10}^{-10}}$

$\Rightarrow U=2.188\times {10}^{6}m/s$