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:
$a. x=8 \mathrm{fm}$
$F=K q^2 r^2=9 \times 109 \times(1.6 \times 10-19)^2(8 \times 10-15)$
$=3.6 \mathrm{NFN}$
$=0.05 \mathrm{NFNFC}=0.053 .6=0.0138 \mathrm{~N}$
$b. x=4 \mathrm{fm}$
$\text { FC }=9 \times 109 \times(1.6 \times 10-19)^2(4 \times 10-15)$
$=23.04 \times 10-29(4 \times 10-15)=14.4 \mathrm{NF}$
$=1 \text { NFNFC }=114.4=0.0694 \mathrm{~N}$
$c. x=2 \mathrm{fm}$
$\mathrm{FC}=9 \times 109 \times(1.6 \times 10-19)^2(2 \times 10-15)$
$=57.6 \mathrm{NFN}=10 \mathrm{NFNFC}=1057.6=0.173$
$\text { d. } x=1 \mathrm{fm}$
$\mathrm{FC}=9 \times 109 \times(1.6 \times 10-19)^2(1 \times 10-15)^2$
$=230.4 \mathrm{NFN}=1000 \mathrm{NFNFC}=1000230.4=4.34$

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