$\frac{x}{x+4}$ is the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its

(i) third permitted energy level to the second level and

(ii) the highest permitted energy level to the second permitted level.

The value of x will be ________.

According to definition of atomic energy, we can write

$E_1=E_0\left(\frac{1}{2^2}-\frac{1}{3^2}\right)=\frac{5E_0}{36},and{E}_2=E_0\left(\frac{1}{2^2}-\frac{1}{{\infty }^2}\right)$

$\frac{E_1}{E_2}=\frac{5}{9}\Rightarrow \frac{x}{x+4}=\frac{5}{5+4}\Rightarrow x=5$

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