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

A) $- \ 3.4\ eV$
B) $- \ 6.8\ eV$
C) $6.8\ eV$
D) 3.4$\ eV$
Explanation

(d) Kinetic energy of electron
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ K\ = \frac{{Ze}^{2}}{8\pi\varepsilon_{0}r}$
Potential energy of electron
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ U\ =$ $\frac{1}{4\pi\varepsilon_{0}r}\frac{{Ze}^{2}}{r}$
$\therefore$ Total energy
$E\ = \ K\ + U\ =$ $\frac{{Ze}^{2}}{8\pi\varepsilon_{0}r} - \ \frac{{Ze}^{2}}{4\pi\varepsilon_{0}r}$
Or $\ \ \ \ \ \ \ \ \ \ \ \ \ E =$ $\frac{{Ze}^{2}}{8\pi\varepsilon_{0}r}$
Or $\ \ \ \ \ \ \ \ \ \ \ \ \ \ E = - K$
Or $\ \ \ \ \ \ \ K = - E = \ - ( - 3.4)$
Or $\ \ \ \ \ \ \ \ \ \ \ \ \ \ = 3.4\ eV$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.

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