An electron, e1 is moving in the fifth stationary state, and another electron e2 is moving in the fourth stationary state. The radius of orbit of electron, e1 is five times the radius of orbit of electron, e2 calculates the ratio of velocity of electron e1 (v1 ) to the velocity of electron e2 (v2).
(a) 5 : 1
(b) 4 : 1
(c) 1 : 5
(d) 1 : 4
Answer: (d) 1 : 4
Explanation:
From the expression of Bohr’s theory, we know that
\(m_ev_1r_1 \) = \(n_1\frac{h}{2 \pi}\) and
\(m_ev_2r_2 \) = \(n_2\frac{h}{2 \pi}\)
\(\frac{m_ev_1r_1}{m_ev_2r_2}\) = \(\frac{n_1}{n_2}\) \(\frac{h}{2 \pi}\) x \(\frac{2 \pi}{h}\)
Given, r1 = 5r2, n1 = 5, n2 = 4
\(\frac{m_e \times v_1 \times 5r_2}{m_e \times v_2 \times r_2}\) = \(\frac{5}{4}\)
⇒ \(\frac{v_1}{v_2}\) = \(\frac{5}{4 \times 5}\) = \(\frac{1}{4}\)
= 1:4