A) \[-\frac{{{e}^{2}}}{4\pi {{\varepsilon }_{0}}r}\]
B) \[\frac{{{e}^{2}}}{4\pi {{\varepsilon }_{0}}r}\]
C) \[\frac{{{e}^{2}}}{8\pi {{\varepsilon }_{0}}r}\]
D) \[-\frac{{{e}^{2}}}{8\pi {{\varepsilon }_{0}}r}\]
Correct Answer: D
Solution :
Centripetal force on electron is |
\[\frac{m{{v}^{2}}}{r}=\frac{{{e}^{2}}}{4\pi {{\varepsilon }_{0}}r}\] |
So, \[m{{v}^{2}}=\frac{{{e}^{2}}}{4\pi {{\varepsilon }_{0}}r}\] |
Kinetic energy \[=\frac{1}{2}m{{v}^{2}}=\frac{{{e}^{2}}}{8\pi {{\varepsilon }_{0}}r}\] |
Potential energy \[=\frac{1}{4\pi {{\varepsilon }_{0}}}\cdot \frac{e}{r}(-e)=-\frac{{{e}^{2}}}{4\pi {{\varepsilon }_{0}}r}\] |
Total energy = Kinetic energy+ Potential energy |
\[\frac{{{e}^{2}}}{8\pi {{\varepsilon }_{0}}r}-\frac{{{e}^{2}}}{\pi {{\varepsilon }_{0}}r}=\frac{{{e}^{2}}-2{{e}^{2}}}{8\pi {{\varepsilon }_{0}}r}=\frac{-{{e}^{2}}}{8\pi {{\varepsilon }_{0}}r}\] |
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