Question

A mono electronic species in energy level with energy 'X' was provided with excess of energy so that it jumps to higher energy level with energy Y. If it can emit 6 wavelengths originated from all possible transitions between these groups levels, then which of the following relation is correct:
(Here n is the principal quantum of energy level X)

• A. $X/Y=(n-1{)}^2$
• B. $X/Y=1+3/n$
• C. $\sqrt{\left(X/Y\right)}=1+3/n$
• D. $X/Y=n/6$

Answer 1

The correct option is C $\sqrt{\left(X/Y\right)}=1+3/n$

As shown in the above diagram, number of possible transitions/emitted wavelengths from ${(n+i)}^{th}$ energy level to $n^{th}$ level is given by:

$=1+2+\mathrm{3..}+i=\sum i=\frac{i(i+1)}{2}$

Solving the above expression for six emitted wavelengths as:

$6=\frac{i(i+1)}{2}{i}^2+i-12=0i=3$

Therefore, $E_X=-R_H\left(\frac{Z^2}{n^2}\right)and{E}_Y=-R_H\left[\frac{Z^2}{{(n+3)}^2}\right]\frac{E_X}{E_Y}=\frac{X}{Y}=\frac{{(n+3)}^2}{n^2}\sqrt{X/Y}=1+3/n$

Hence, option C is the correct answer