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GUJCET · Physics · Atoms
Kinetic energy of the electron in hydrogen atom is \(\frac{e^{2}}{8 \pi \varepsilon_{0} r}\) ．Then its potential energy is _________ ．
- 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 \(-\frac{e^{2}}{8 \pi \varepsilon_{0} r}\)
Answer & Solution
Correct Answer
(B) \(-\frac{e^{2}}{4 \pi \varepsilon_{0} r}\)
Step-by-step Solution
Detailed explanation
\(-\frac{e^{2}}{4 \pi \varepsilon_{0} r}\)
Potential energy
\(\mathrm{U}=-2 \times\) Kinetic energy
\(\mathrm{U}=-2 \times \frac{1}{8 \pi \varepsilon_{0}} \cdot \frac{e^{2}}{r}\)
\(\mathrm{U}=-\frac{e^{2}}{4 \pi \varepsilon_{0} r}\)
Potential energy
\(\mathrm{U}=-2 \times\) Kinetic energy
\(\mathrm{U}=-2 \times \frac{1}{8 \pi \varepsilon_{0}} \cdot \frac{e^{2}}{r}\)
\(\mathrm{U}=-\frac{e^{2}}{4 \pi \varepsilon_{0} r}\)
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