Answer:
a
[tex]PE = 2.3 *10^{-16} \ J[/tex]
b
[tex]T = 1.1 *10^{7} \ K[/tex]
Explanation:
From the question we are told that
The distance of separation is [tex]d = 1.00 *10^{-12} \ m[/tex]
Generally the electric potential energy can be mathematically represented as
[tex]PE = \frac{k * q_1 q_2 }{d}[/tex]
Given that in a nuclei the only charged particle is the proton who charge is
[tex]p = 1.60 *10^{-19} \ C[/tex]
Hence
[tex]q_1 = q_2 = 1.60 *10 ^{-19} \ C[/tex]
And k is the coulomb constant with values [tex]k = 9*10^{9} \ kg\cdot m^3\cdot s^{-4}\cdot A^2.N/A2[/tex]
So we have that
[tex]PE = \frac{9*10^9 * (1.60 *10^{-19})^2}{ 1.00*10^{-12}}[/tex]
[tex]PE = 2.3 *10^{-16} \ J[/tex]
The relationship between the electrical potential energy and the temperature is mathematically represented as
[tex]PE = \frac{3}{2} kT[/tex]
Here k is the Boltzmann's constant with value [tex]k = 1.38*10^{-23} JK^{-1}[/tex]
making T the subject
[tex]T = \frac{2}{3} * \frac{PE}{k}[/tex]
substituting values
[tex]T = \frac{2}{3} * \frac{2.30 *10^{-16}}{ 1.38 *10^{-23}}[/tex]
[tex]T = 1.1 *10^{7} \ K[/tex]
