Question 11 Mark

Suppose the magnitude of Nuclear force between two protons varies with the distance between them as shown in figure. Estimate the ratio "Nuclear force Coulomb force" for:

1. $x = 8fm$
2. $x = 4fm$
3. $x = 2fm$
4. $x = 1fm (1fm = 10^{-15}m). $

Answer

First let us calculate the coulomb force between $2$ protons for distance:

1. $x = 8fm$

$F = K q^2r^{2 }= 9 \times 109 \times (1.6 \times 10 - 19)^2(8 \times 10 - 15)$
$= 3.6\ \text{NFN}$
$= 0.05\  \text{NFNFC}= 0.053.6 = 0.0138 N$

2. $x = 4fm$

$FC = 9 \times 109 \times (1.6 \times 10 - 19)^2(4 \times 10 - 15)$
$= 23.04 \times 10 - 29(4 \times 10 - 15) = 14.4\ NF$
$= 1\ \text{NFNFC} = 114.4 = 0.0694N$

3. $x = 2fm$

$FC = 9 \times 109 \times (1.6 \times 10 - 19)^2(2 \times 10 - 15)$
$= 57.6\  \text{NFN}$
$= 10\  \text{NFNFC} = 1057.6 =0.173$

4. $x = 1fm$

$FC = 9 \times 109 \times (1.6 \times 10 - 19)^2(1 \times 10 - 15)^2$
$= 230.4\ \text{NFN}  $
$= 1000\  \text{NFNFC} = 1000230.4 = 4.34$

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