Question

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

Answer 1

In the $1^{st}$ Bohr orbit of $H$ :
$v = 2.18 \times 10^{6}$ ms$^{-1}$.
Now, let us consider that in $Li^{2+}$ the electron is in $n^{th}$ orbit. Speed of electron in $n^{th}$ Bohr orbit of $Li^{2+}$ is
$v = \left(Li^{2+}\right) = 2.18 \times10^{6}\times\frac{3}{n}$
Now, applying the condition of equal speed
$2.18 \times10^{6} \times\frac{3}{n} = 2.18 \times10^{6}$
$\Rightarrow n =3$