First slide

Electrostatic potential energy

Question

Suppose two deuterons must get as close as 10^-14 m in order for the nuclear force to overcome the repulsive electrostatic force. The height of the electrostatic barrier is nearest to

Easy

A

0.14 MeV
B

2.3 MeV
C

1.8 MeV
D

0.56 MeV

Solution

deutron is having one proton + one neutron
so charge of deutron is $1.602 \times 10^{- 19} C$
Barrier height
$\begin{array}{rcl} = & \frac{1}{4 π ε_{0}} \frac{e^{2}}{r_{e}} J = \frac{1}{4 π ε_{0}} \frac{e}{r_{e}} eV \end{array}$
$\begin{array}{rcl} = & \frac{9 \times 10^{9} \times 1.6 \times 10^{- 19}}{10^{- 14}} eV = 1.44 \times 10^{5} eV = 0.14 MeV \end{array}$

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