Question

A monoelectronic species in an energy level with an energy of X was provided with an excess of energy so that it jumps to a higher energy level having energy Y. If it can emit six wavelengths originating from all possible transitions between these group levels, then which of the following relation is correct?

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

Answer 1

The correct option is A $\sqrt{\frac{X}{Y}}=1+\frac{3}{n}$

If 'n' is the principal quantum number of the energy level corresponding to energy X, then the energy level Y will be having the principal quantum number n+3 (since it has a total of 6 possible transitions).
$X\propto \frac{1}{n^2}$ and $Y\propto \frac{1}{(n+3{)}^2}$
$\frac{X}{Y}=\frac{(n+3{)}^2}{n^2}$
$\Rightarrow \sqrt{\frac{X}{Y}}=1+\frac{3}{n}$