Question

An electron, $e_1$ is moving in the fifth stationary state, and another electron $e_2$ is moving in the fourth stationary state. The radius of orbit of electron, $e_1$ is five times the radius of orbit of electron, $e_2$ calculate the ratio of velocity of electron $e_1\left(v_1\right)$ to the velocity of electron $e_2\left(v_2\right)$.

• A. 5 : 1
• B. 4 : 1
• C. 1 : 5
• D. 1 : 4

Answer 1

Answer: (D)

From the expression of Bohr’s theory, we know that
m_e v₁ r₁ = n₁ $\frac{h}{2}$
& m_e v₂ r₂ = n₂ $\frac{h}{2}$
$\frac{m_e{v}_1{r}_1}{m_e{v}_2{r}_2}=\frac{n_1}{n_2}$
Given, r₁ = 5 r₂, n₁ = 5, n₂ = 4
$\frac{m_e{v}_{1}5r_2}{m_e{v}_2{r}_2}=\frac{5}{4}$
$\frac{v_1}{v_2}=\frac{5}{45}=\frac{1}{4}=1:4$