Question

What is the ratio of distance between ‘L’ and ‘M’ orbits in He^+1 to the distance between ‘M’ and ‘N’ orbits in Li^+2

Answer 1

Given that,

The distance between L and M orbits in He⁺¹

The distance between M and N orbits in Li⁺²

We know that,

K, L, M, N is orbit state.

K = 1, L = 2, M = 3, N = 4

(I). We need to calculate the distance L

Using formula of distance

$r_{2}= 0.529\times\dfrac{n^2}{Z}\ \AA$

Put the value into the formula

$r_{2}=0.529\times\dfrac{2^2}{2}$

$r_{2}=1.058$

We need to calculate the distance M

Using formula of distance

$r_{3}= 0.529\times\dfrac{n^2}{Z}\ \AA$

Put the value into the formula

$r_{3}=0.529\times\dfrac{3^2}{2}$

$r_{3}=2.3805$

We need to calculate the distance between ‘L’ and ‘M’ orbits

Using formula of distance

$r=r_{3}-r_{2}$

Put the value into the formula

$r=2.380- 1.058$

$r=1.322$

(II). We need to calculate the distance M

Using formula of distance

$r_{3}= 0.529\times\dfrac{n^2}{Z}\ \AA$

Put the value into the formula

$r_{3}=0.529\times\dfrac{3^2}{3}$

$r_{3}=1.587$

We need to calculate the distance N

Using formula of distance

$r_{4}= 0.529\times\dfrac{n^2}{Z}\ \AA$

Put the value into the formula

$r_{4}=0.529\times\dfrac{4^2}{3}$

$r_{4}=2.821$

We need to calculate the distance between M and N orbits

Using formula of distance

$r'=r_{4}-r_{3}$

Put the value into the formula

$r'=2.821- 1.587$

$r'=1.234$

We need to ratio of the distance between L and M orbits in He⁺¹ to the distance between M and N orbits in Li⁺²

Using ratio of distance

$\dfrac{r}{r'}=\dfrac{1.322}{1.234}$

$\dfrac{r}{r'}=\dfrac{661}{617}$

Hence, the distance between L and M orbits in He⁺¹ to the distance between M and N orbits in Li⁺² is 661:617