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The total energy of an electron in the first excited state of the hydrogen is about $-3.4 \mathrm{eV}$.
(a) What is the kinetic energy of the electron in this state?
(b) What is the potential energy of the electron in this state?
(c) Which of the answers above would change if the choice of the zero of potential energy is changed?
(a) What is the kinetic energy of the electron in this state?
(b) What is the potential energy of the electron in this state?
(c) Which of the answers above would change if the choice of the zero of potential energy is changed?
Solution:
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Verified Answer
We know, Kinetic energy of electron
$$
=\frac{1}{4 \pi \varepsilon_0} \frac{7 e^2}{2 \mathrm{r}}
$$
Potential energy $=-2($ K. E. $)$
Total energy $=$ P. E. $+\mathrm{K}$. E. $=-\mathrm{K}$. E. where electric potential would be zero at infinity.
(a) Total energy $=-3.4 \mathrm{eV}$
$$
\Rightarrow \mathrm{K} . \mathrm{E}=-(-3.4)=+3.4 \mathrm{eV} \text {. }
$$
(b) P. E. $=-2 \mathrm{~K}, \mathrm{E}=-6.8 \mathrm{eV}$
(c) If zero of potential is changed then K. E. which is independent of this choice remains same whereas P. E. and hence total energy of the state would change.
$$
=\frac{1}{4 \pi \varepsilon_0} \frac{7 e^2}{2 \mathrm{r}}
$$
Potential energy $=-2($ K. E. $)$
Total energy $=$ P. E. $+\mathrm{K}$. E. $=-\mathrm{K}$. E. where electric potential would be zero at infinity.
(a) Total energy $=-3.4 \mathrm{eV}$
$$
\Rightarrow \mathrm{K} . \mathrm{E}=-(-3.4)=+3.4 \mathrm{eV} \text {. }
$$
(b) P. E. $=-2 \mathrm{~K}, \mathrm{E}=-6.8 \mathrm{eV}$
(c) If zero of potential is changed then K. E. which is independent of this choice remains same whereas P. E. and hence total energy of the state would change.
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