# Find the Speed of the Electron in the Ground State of a Hydrogen Atom. the Description of Ground State is Given in the Previous Problem. - Physics

Short Note

Find the speed of the electron in the ground state of a hydrogen atom. The description of ground state is given in the previous problem.

#### Solution

Given:
Separation between the two charges, r = 0.53 Å = 0.53 × 10−10 m
By Coulomb's Law, force,

$F = \frac{1}{4\pi \epsilon_0}\frac{q_1 q_2}{r^2}$

Here,

$q_1 = q_2 = e$

$\Rightarrow F = \frac{9 \times {10}^9 \times \left( 1 . 6 \times {10}^{- 19} \right)^2}{\left( 0 . 53 \times {10}^{- 10} \right)^2}$

$= 8 . 2 \times {10}^{- 8} N$

Now, mass of an electron, Me = 9.12 × 1031 kg
The necessary centripetal force is provided by the Coulombian force.

$\Rightarrow F_e = \frac{M_e v^2}{r}$

$\Rightarrow v^2 = 0 . 4775 \times {10}^{13}$

$= 4 . 775 \times {10}^{12}$

$\Rightarrow v = 2 . 18 \times {10}^6$  m/s

Is there an error in this question or solution?

#### APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 7 Electric Field and Potential
Q 19 | Page 121