Correct Answer - Option 4 : c/137
CONCEPT:
- The Bhor atom model consists of a small positive nucleus surrounded by negatively charged electrons moving in orbits. The major postulates made by Bhor according to his model are
-
Electrons revolve around the nucleus in a circular path called shells
- The electrons get displaced from the lower energy level to the higher energy level by absorbing energy and gets de excited vice versa
- The angular momentum in the orbits is quantized and is given by
\(\Rightarrow mvr = \frac{nh}{2\pi}\)
\(\Rightarrow V = \frac{n h}{2\pi m r}\)
Where V = Velocity of electrons, h = Plancks constant, m = mass, r = radius of the orbit
CALCULATION:
Given - h = 6.62 × 10-34 Js, m = 9.1× 10-31 Kg, and n = 1
- The radius of the first orbit is given by
\(\Rightarrow r_{n} =n^{2} a_{0}\)
Substituting the value n = 1
\(\Rightarrow r_{n} = 1^{2}\times a_{0} = a_{0} = 0.529 A^{0}\) [ we know a0 = 0.529 A0]
- The velocity of the electron revolving in the orbit is given by
\(\Rightarrow V = \frac{n h}{2\pi m r}\)
Substituting the given values in the above equation
\(\Rightarrow V = \frac{6.626\times10^{-34}}{2\times 3.14\times 9.1\times 10^{-31}\times 0.529\times 10^{-10 }} = 2.189\times 10^{6} m/s\)
Converting V in terms of C
\(\Rightarrow \frac{V}{C} = \frac{2.189\times 10^{6}}{3\times 10^{8}} = \frac{1}{137}\)
\(\Rightarrow \frac{V}{C} = \frac{1}{137}\)
\(\Rightarrow V = \frac{C}{137}\)
- Hence, option 4 is the answer
