Question

A monoelectronic 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 six wavelengths originated from all possible transition between these group levels, then which of the following relation is correct?
(where $n$ is the principal quantum number of energy level X).

• 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

Answer: (A)

If $n$ is the principal quantum number of energy level corresponding to energy $X$, the principal quantum number of energy level $Y$ is $(n+3)$ as it emit six wavelengths.

$\frac{X}{Y}=\frac{(n+3)^{2}}{n^{2}} $

$\Rightarrow \sqrt{\frac{X}{Y}}=1+\frac{3}{n}$