Question

Calculate the radii of 2nd Bohr orbit of Li2+.​

Answer 1

We have to Calculate the radius of 2nd Bohr's orbit of Li²⁺ ion.

A/c to Bohr's atomic theory,

• Electrostatic force acting on an electron revolved around the nucleus which is balanced by centripetal force acting on it.
• an electron revolves in an orbit has angular momentum which is integral multiple of $\frac{h}{2\pi}$

from above two important postulations about atomic theory, we are able to find radius of orbit.

we get mathematical expression to find radius of nth orbit of Hydrogen like ion and that is..

$r_n=\frac{n^2h^2}{4\pi^2mZKe^2}$

after putting values of h, π , m , K and e we get,

$\quad r_n=0.529\times\frac{n^2}{Z} A^{\circ}$

here n denotes no of nth orbit and Z is atomic number of ion.

for 2nd orbit of Li²⁺ ion,

n = 2 and Z = 3

∴ r₂ = $0.529\times\frac{2^2}{3}$ Å

= $0.529\times\frac{4}{3}$ Å

= 0.7053 Å

Therefore the radius of 2nd orbit of Li²⁺ ion is 0.7053 Å.