Question

Determine the Bohr orbit of $L{i}^{2+}$ ion in which electron is moving at speed equal to the speed of electron in the first Bohr orbit of H-atom

Answer 1

Answer: 3

In the $1^{st}$ Bohr orbit of $H$ :
$v=2.18\times 10^6$ ms${}^{-1}$.
Now, let us consider that in $L{i}^{2+}$ the electron is in $n^{th}$ orbit. Speed of electron in $n^{th}$ Bohr orbit of $L{i}^{2+}$ is
$v=\left(L{i}^{2+}\right)=2.18\times 10^6\times \frac{3}{n}$
Now, applying the condition of equal speed
$2.18\times 10^6\times \frac{3}{n}=2.18\times 10^6$
$\Rightarrow n=3$