1. Tardigrade
  2. Question
  3. Chemistry
  4. 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 calculate the ratio of velocity of electron e1(v1) to the velocity of electron e2(v2).

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Q. 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 $e_{2}\left(v_{2}\right)$.

JIPMERJIPMER 2018Structure of Atom

Solution:

From the expression of Bohr’s theory, we know that
me v1 r1 = n1 $\frac{h}{2}$
& me 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
$\frac{m_{e}\,\,v_{1}\,\,5r_{2}}{m_{e}\,\,v_{2}\,\,r_{2}}=\frac{5}{4}$
$\frac{v_{1}}{v_{2}}=\frac{5}{4\,\,5}=\frac{1}{4}=1: 4$