AP EAMCET201920 Apr 2019Morning ShiftPhysicsAtomic PhysicsActual
In a system, a particle (A ) of mass (m ) and charge (-2 q ) is moving in the nearest orbit around a very heavy particle (B ) having charge (+q ). Assuming Bohr's model of the atom to be applicable to this system, the orbital angular velocity of the particle (A ) is
Options
- A( 2 m^2 q^2 ₀ h^4 )
- B( 3 m^3 q^2 ₀^3 h^2 )
- C( 2 m q^4 ₀^2 h^3 )
- D( 5 m^2 q^3 ₀^3 h^2 )
Correct answer
C. ( 2 m q^4 ₀^2 h^3 )
Step-by-step solution
In a system, a particle (A ) moving around a particle (B ) in a circular path then applied the centripetal force directed and center of the circular path. So, the electric force, (F_e= ) centripetal force, (F_c ) ( k q₁ q₂ r^2 =m r ^2 ) ...(i) Given, ( q₁=2 q, q₂=q ) and (k= 1 4 ₀ ) Putting these values in Eq. (i), we get ( 1 4 ₀ q(2 q) r^2 =m r ^2 ) ...(ii) According to the Bohr's model, (m v r= n h 2 m r^2 = n h 2 (iii) [ = v r ] ) (iii) ( [ = v r ] ) From Eqs. (ii) and (iii), we get ( = 2 m q^4 ₀^2 h^3 [ n =1] )