Question

Total energy of an electron in an atom is _____________.
(A) less than zero
(B) more than zero
(C) may be less or more than zero
(D) none of the above

Answer 1

As we know that Bohr introduced an atomic model which shows that the electrons in atoms are in circular orbits of differing energy around the nucleus. He used the term shells (or energy levels) to describe these orbits of differing energy. He said that the energy of an electron is quantized which means electrons can have one energy level or another but not between them. So we will use Bohr atomic model to calculate the nature of total energy of an electron.

Complete answer:
Let us first discuss about Bohr atomic model:-
-According to this model, an atom consists of electrons orbiting around the small, dense nucleus in certain energy levels (shells) just like planets orbiting around the Sun in the Solar system. These electrons are restricted to these shells. These electrons can jump from one level to another but not anywhere between them.
-Considering all the laws and theories, Bohr derived energy of an electron revolving around the nucleus as follows:-
E = $\dfrac{-13.6{{Z}^{2}}}{{{n}^{2}}}eV$
where,
Z = atomic number of the atom
n = the energy level (shell) in which electron is orbiting (or the principal quantum number)
-Since we know that the value of atomic number of an atom as well as the energy level of an electron revolving around the nucleus will always be a positive integral value , so E = $\dfrac{-13.6{{Z}^{2}}}{{{n}^{2}}}eV$ will always be negative i.e., less than zero.

Hence the total energy of an electron in an atom is (A) less than zero.

Note:
Always remember that the Bohr atomic model works well for very simple atoms such as hydrogen or hydrogen like atoms (which has 1 electron) but not for more complex atoms.
-Also when an electron jumps from lower to higher energy level, it absorbs the energy whereas if it jumps from higher to lower energy level, it releases the energy.