Question

In the Bohr’s model hydrogen atom, the electron moves around the nucleus in a circular orbit of radius \[5 \times {10^{ - 11}}\] meters. If its time period is \[1.5 \times {10^{ - 16}}\sec \] , then the current associated with the electron motion is
a.) Zero
b.) \[1.6 \times {10^{ - 19}}A\]
c.) \[0.17A\]
d.) \[1.7 \times {10^{ - 3}}A\]

Answer 1

Hint: According to Bohr’s model of the hydrogen atom, the electron revolves around the nucleus in circular orbits. The magnitude of the charge of an electron is \[1.6 \times {10^{ - 19}}C\] . The current associated with the motion of an electron in this case is \[Current = \dfrac{{Charge{\text{ }}of{\text{ }}an{\text{ }}electron}}{{Time{\text{ }}period{\text{ }}of{\text{ }}revolution{\text{ }}of{\text{ }}an{\text{ }}electron}}\] .

Complete step by step answer:
In this problem, we are required to calculate the current associated with the motion of an electron for an electron that moves around in a circular orbit as described in the Bohr’s model of the hydrogen atom, so it will be good to start by describing what the Bohr’s model of hydrogen atom looks like.
Bohr’s model of a hydrogen atom depicts the structure of an atom in reference to a hydrogen atom. According to Bohr’s model of a hydrogen atom in the center of an atom lies a nucleus that contains all the nucleons (the protons and the neutrons). The electrons revolve around the nucleus in fixed circular stationary objects, in these stationary orbits, the electrons have a fixed speed and hence angular momentum.

Now we know that current at any point is equal to the charge passing through that point in \[1\sec \] .
We also know that the magnitude of the charge on an electron is \[1.6 \times {10^{ - 19}}C\] and it is given that it requires \[1.5 \times {10^{ - 16}}\sec \] to complete a full revolution around the nucleus.
So, the current associated with the motion of an electron is given by the equation
\[Current = \dfrac{{Charge{\text{ }}of{\text{ }}an{\text{ }}electron}}{{Time{\text{ }}period{\text{ }}of{\text{ }}revolution{\text{ }}of{\text{ }}an{\text{ }}electron}}\]
\[Current = \dfrac{{1.6 \times {{10}^{ - 19}}}}{{1.5 \times {{10}^{ - 16}}}}\]
\[Current = 1.7 \times {10^{ - 3}}A\]
So, the current associated with an electron revolving around the nucleus with a time period of \[1.5 \times {10^{ - 16}}\sec \] is \[1.7 \times {10^{ - 3}}A\] .
So, the correct answer is “Option D”.

Note: Bohr’s model of a hydrogen atom is important but has a lot of shortcomings too. It could not explain the presence of multiple spectral lines of the hydrogen atom, it could explain the dual nature of matter, and it could not explain the uncertainty principle and the quantization of energy.