Question

10. Calculate the distance between an alpha particle and an electron in air if they attract each other with a force of 6 x 10to the power -11 newton.​

Answer 1

Given :

The force of attraction between an alpha particle and an electron in air is :

= $6 \times 10^{-11} N$

To Find :

Distance between the electron and the alpha particle in air  is = ?

Solution :

Since we know that the formula for the electrostatic force of attraction between two particles is given as :

$F = \frac{Kq_1 q_2}{r^2}$     -(1)

Here $q_1 , q_2$ are the charges on the two particles and r is the distance between them and K = $\frac{1}{4 \pi \epsilon_0}$  is constant .

Now , we know that charge on a electron is e and charge on a alpha particle is 2e , where e$= 1.6 \times 10_{-19}C$

So , using eq 1 and putting the given values we can write ;

$6 \times 10^{-11}$ $= \frac{1}{4\pi \epsilon_0}\times \frac{e \times 2e}{r^2}$

Or, $6 \times 10^{-11}= \frac{9 \times 10^9 \times 2.e^2}{r^2}$

Or, $r^2= \frac{9 \times 10^9 \times (1.6 \times 10^{-19})^2}{6 \times 10^{-11}}$

or, $r^2 = \frac{9\times 10^9 \times 2 \times 2.56 \times 10^{-38}}{6 \times 10^{-11}}$

Or,$r^2 = \frac{9 \times 2 \times 2.56 \times 10^{-18}}{6}$

Or , $r = \sqrt{2.56 \times 10^{-18}}$

⇒$r = 1.6 \times 10^{-9} m$

So , the distance between the electron and the alpha particle is $r = 1.6 \times 10^{-9} m$ .

Answer 2

The distance between the electron and alpha particle is r = 1.6 x 10^-9 m

Explanation:

The electrostatic force of attraction between two particles is given by:

F = Kq1q2 / r^2     -------(1)

Here q1 , q2 charges and r is the radius and K = 1/4πεo is constant.

We know that charge on electron = e

Charge on alpha particle = 2e

e =  1.6 x 10^-19 C

Now put the values in equation (1).

6 x 10^-11 = 1 / 4πεo x e x 2e / r^2

6 x 10^-11  = 9 x 10^9 x 2e^2 / r^2

r^2 =  9 x 10^9 x ( 1.6 x 10^-19)^2 / 6 x 10^-11

r^2 = 9 x 10^9 x 2 x 2.56 x 10^-38 / 6

r = √ 2.56 x 10^-18

r = 1.6 x 10^-9 m

Hence the distance between the electron and alpha particle is r = 1.6 x 10^-9 m