An electron makes a transition from \(n=2\) level to \(n=1\) level in the Bohr model of a hydrogen atom. Its period of r…

Explanation\( \text{Given: Electron transition from } n = 2 \to n = 1 \) \( \text{In the Bohr model:} \quad r_n \propto n^2, \quad v_n \propto \frac{1}{n} \) \( T_n = \frac{2\pi r_n}{v_n} \propto \frac{n^2}{1/n} = n^3 \) \( \text{Hence, } T_n \propto n^3 \) \( \frac{T_2}{T_1} = \left(\frac{2}{1}\right)^3 = 8 \) \( \text{When the electron goes from } n=2 \text{ to } n=1, \text{ the period becomes } \frac{1}{8} \text{ of its initial value.} \) \( \text{Percentage decrease} = \frac{T_2 - T_1}{T_2} \times 100 = \frac{8T_1 - T_1}{8T_1} \times 100 = \frac{7}{8} \times 100 = 87.5\% \)