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JIPMER 2007
Exam
JIPMER
Year
2007
Subject
Physics
Chapter
Atomic Physics

JIPMER 2007 · Physics · Atomic Physics

The total energy of an electron in the first excited state of...

The total energy of an electron in the first excited state of hydrogen is about −3.4-3.4 eV . Its kinetic energy in this state is

Options

  1. A−3.4eV-3.4 \mathrm{eV}
  2. B−6.8eV-6.8 \mathrm{eV}
  3. C6.8eV6.8 \mathrm{eV}
  4. D3.4eV3.4 \mathrm{eV}

Correct answer

D. 3.4eV3.4 \mathrm{eV}

Step-by-step solution

The kinetic energy is equal to the negative of total energy. Kinetic energy of electron K=Ze28πε0rK=\frac{Z e^2}{8 \pi \varepsilon_0 r} Potential energy of electron U=−14πε0Ze2rU=-\frac{1}{4 \pi \varepsilon_0} \frac{Z e^2}{r} :. Total energy E=K+U=Ze28πε0r−Ze24πε0rE=K+U=\frac{Z e^2}{8 \pi \varepsilon_0 r}-\frac{Z e^2}{4 \pi \varepsilon_0 r} or E=−Ze28πε0r or E=−K or K=−E=−(−3.4)=3.4eV\begin{aligned} & \text{ or } E=-\frac{Z e^2}{8 \pi \varepsilon_0 r} \\ & \text{ or } E=-K \\ & \text{ or } K=-E=-(-3.4)=3.4 \mathrm{eV} \\ & \end{aligned}$$
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