Answer:
[tex]Ep=-2.3*10^{-19}J[/tex]
Explanation:
The change in potential energy can be expressed as:
[tex]Ep=K.\frac{q1.q2}{r}[/tex]
where K is a constant with a value of [tex]9*10^{9}\frac{N.m^{2}}{C^{2}}[/tex], q1 and q2 are the charges of the proton and the electron and r is the distance between them.
The charge for the proton is [tex]+1.6*10^{-19}C[/tex] and the charge for the electron is [tex]-1.6*10^{-19}C[/tex].
Converting r=1.0nm to m:
[tex]1.0nm*\frac{1*10^{-9}m}{1.0nm}=1*10^{-9}m[/tex]
Replacing values:
[tex]Ep=9*10^{9}\frac{N.m^{2}}{C^{2}}.\frac{(+1.6*10^{-19}C).(-1.6*10^{-19}C)}{1*10^{-9}m}[/tex]
[tex]Ep=-2.3*10^{-19}J[/tex]
