Question

17. Calculate the speed of electron revolving around the nucleus of a hydrogen atom in order that it
may not be pulled into the nucleus by electrostatic attraction.​

Answer 1

Here in this case the speed of the electron is ,

v=2πr1TNow , r1=0⋅0529×10−9 mT=1⋅519×10−16 sSo the speed is , v=2π×0⋅0529×10−91⋅519×10−16 =2⋅19×106 m/s

Answer 2

The speed of the electron revolving around the nucleus of hydrogen atom in order that it may not be pulled into the nucleus by electrostatic attraction is  $2.25 \times 10^{6} \ \text{m}/\text{s}$

Explanation:

Data

$\text{Mass of elcrton} \ (\text{m}_\text{e})= 9.1 \ \times \ 10^{-31} \ \text {kg}$

$\text{Radius of Orbit \ (r)} = 0.5 \times 10^{-10} \ \text{m}$

$\text{ Charge of an electron (e)} = 1.6 \times 10^{-19} \ \text{coulombs}$

Let us take centripetal force is equal to the electrostatic force

$\text{F}_\text{E} = \text{F}_\text{C}$

$\text{F}_\text{E} = \frac{\text{Kq}_1\text{q}_2}{\text{r}^2}$

$\text{Where} \ \text{q}_1 = \text{q}_2 = e$

$\text{F}_\text{E} = \frac{\text{K} \times e^2}{\text{r}^2} --------> (1)$

$\text{F}_\text{C} = \frac{\text{m}_e\text{v}^2}{\text{r}} --------> (2)$

Equate (1) and (2)

$\frac{\text{K} \times e^2}{\text{r}^2} = \frac{\text{m}_e\text{v}^2}{\text{r}}$

$\text{v}^2 = \frac{\text{K} \times e^2}{\text{r} \times {m}_e}$

$\text{v} = \sqrt{\frac{\text{K} \times e^2}{\text{r} \times {m}_e}}$

Substitute the respective values in above equation.

$\text{v} = \sqrt{\frac{9 \times 10^{9} \times(1.6\times 10^{-19})^2}{9.1 \times 10^{-31} \times 0.5 \times 10^{-10}}}$

$\text{v} = 2.25 \times 10^{6} \ \text{m}/\text{s}$

Therefore the speed required by an electron is $2.25 \times 10^{6} \ \text{m}/\text{s}$ , when an electron revolving around the nucleus of a hydrogen atom in order that it may not be pulled into the nucleus by electrostatic attraction.

To Learn More

1) What is an electrostatic force? Why is it called non-contact force?

https://brainly.in/question/1166816

2) If the centripetal force is of the form m^a × v^b × r^c, find the values of a, b and c.

https://brainly.in/question/3802346