Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# In the Bohr Model of Hydrogen Atom, the Electron is Treated as a Particle Going in a Circle with the Centre at the Proton. the Proton Itself is Assumed to Be Fixed in an Inertial Frame. - Physics

#### Question

In the Bohr model of hydrogen atom, the electron is treated as a particle going in a circle with the centre at the proton. The proton itself is assumed to be fixed in an inertial frame. The centripetal force is provided by the Coulomb attraction. In the ground state, the electron goes round the proton in a circle of radius 5.3 × 10−11 m. Find the speed of the electron in the ground state. Mass of the electron = 9.1 × 10−31 kg and charge of the electron = 1.6 × 10−19 C.

Sum

#### Solution

$\text { Given }:$

$\text {Radius of the orbit of the ground state }= r = 5 . 3 \times {10}^{- 11}$ m

$\text { Mass of the electron }= \text{m} = 9 . 1 \times {10}^{- 31} \text{kg}$

$\text { Charge of electron }= q = 1 . 6 \times {10}^{- 19} c$

$\text {We know}:$

$\text {Centripetal force = Coulomb attraction}$

$\text {Therefore, we have :}$

$\Rightarrow \frac{\text{mv}^2}{r} = \frac{1}{4 \pi\epsilon_\circ}\frac{\text{q}^2}{\text{r}^2}$

$\Rightarrow \text{v}^2 = \frac{1}{4 \pi\epsilon_\circ}\frac{q^2}{rm}$

$= \frac{9 \times {10}^9 \times \left( 1 . 6 \times {10}^{- 19} \right)^2}{5 . 3 \times {10}^{- 11} \times 9 . 1 \times {10}^{- 31}}$

$= \frac{23 . 04}{48 . 23} \times {10}^{13}$

$= 0 . 477 \times {10}^{13} = 4 . 7 \times {10}^{12}$

$\Rightarrow v = \sqrt{4 . 7} \times {10}^{12} = 2 . 2 \times {10}^6 \text{m/s}$

Is there an error in this question or solution?

#### APPEARS IN

HC Verma Class 12 Concepts of Physics 1
Chapter 7 Circular Motion
Q 9 | Page 114