AP EAMCET201921 Apr 2019Evening ShiftPhysicsMotion in Two DimensionsActual
In a hydrogen atom, an electron of mass 9 . 1 × 10 - 31 kg revolves about a proton in circular orbit of radius 0 . 53 A . The radial acceleration and angular velocity of electron are respectively
Options
- A9 × 10 22   m   s - 2 , 4 . 1 × 10 16   s - 1
- B4 . 1 × 10 16   m   s - 2 , 9 × 10 22   s - 1
- C9 × 10 16   m   s - 2 , 4 . 1 × 10 22   s - 1
- D4 . 1 × 10 22   m   s - 2 ,   9 × 10 16   s - 1
Correct answer
A. 9 × 10 22   m   s - 2 , 4 . 1 × 10 16   s - 1
Step-by-step solution
The centripetal force is equal to the electrostatic force, when an electron revolves around a proton. m e v 2 r = k q 1 q 2 r 2 Rewrite the above equation. m e v 2 r = k q 1 q 2 m e ( r ω ) 2 r = k q q ω = k q 2 m e r 3 Substitute the given values in the above equation. ω = 9 × 10 9 × 1 . 6 × 10 - 19 2 9 . 1 × 10 - 31 × 0 . 53 × 10 - 10 3 ω = 4 . 1 × 10 16   s - 1 The radial acceleration of the electron can be calculated as, a r = r ω 2 a r = 0 . 53 &