Question

The total energy of an electron in an atom in an orbit is -3.4 eV. Its kinetic and potential energies are, respectively:

Answer 1

Hint: The sum of the potential energy and the kinetic energy equals the total energy of an electron in an atom in an orbit. The kinetic energy equals the negative of the total energy of an electron and the potential energy equals the twice the value of the total energy of an electron.
Formula used:
\[\begin{align}
  & PE=\dfrac{-kZ{{e}^{2}}}{r} \\
 & KE=\dfrac{kZ{{e}^{2}}}{2r} \\
\end{align}\]

Complete answer:
From the given information, we have the data as follows.
The total energy of an electron in an atom in an orbit is -3.4 eV.
We are asked to find the values of the kinetic energy and the potential energy.
The sum of the potential energy and the kinetic energy equals the total energy of an electron in an atom in an orbit.
\[TE=PE+KE\]
The kinetic energy equals the negative of the total energy of an electron
\[KE=-(TE)\]
Substitute the values in the above equation.
\[\begin{align}
  & KE=-(-3.4) \\
 & \therefore KE=3.4eV \\
\end{align}\]
The potential energy equals the twice the value of the total energy of an electron.
\[PE=2(TE)\]
Substitute the values in the above equation.
\[\begin{align}
  & PE=2(-3.4) \\
 & \therefore PE=-6.8eV \\
\end{align}\]
\[\therefore \] The value of the potential energy of electron in an atom of an orbit is, - 6.8 eV and the value of the kinetic energy of electron in an atom of an orbit is, 3.4 eV.

Note: The kinetic energy is half the value of the potential energy with the sign being reversed. The kinetic energy equals the negative of the total energy of an electron and the potential energy equals the twice the value of the total energy of an electron. The sum of the potential energy and the kinetic energy equals the total energy of an electron in an atom in an orbit.