The electrostatic force of attraction between electron and nucleus is a central force which provides necessary centripetal force for the circular motion of the electron.
The simple Bohr model cannot be directly applied to calculate the energy levels of an atom with many electrons. This is because of the electrons not being subject to a central force.
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Explanation:

The Bohr model of the atom was proposed by Niels Bohr in 1913 and successfully explained the emission spectrum of hydrogen. However, this model cannot be directly applied to calculate the energy levels of atoms with many electrons for several reasons. The correct answer to the given question is option a) "because of the electron not being subject to a central force." Let's dive into the details:

1. Electrons not subject to a central force:
In the Bohr model, electrons are assumed to move in circular orbits around the nucleus, similar to planets orbiting the Sun. The centripetal force required to keep the electron in its orbit is provided by the electrostatic attraction between the negatively charged electron and the positively charged nucleus. However, in an atom with many electrons, each electron is influenced not only by the nucleus but also by the repulsion from other electrons. This results in a complex interaction between the electrons, and they are not subject to a simple central force. Therefore, the Bohr model cannot accurately describe the energy levels of multi-electron atoms.

2. Electrons colliding with each other:
In addition to the repulsion between electrons due to their negative charges, electrons can also collide with each other. These collisions can affect the energy levels and behavior of the electrons. The Bohr model does not account for these collisions, making it inadequate for calculating the energy levels of atoms with many electrons.

3. Screening effect:
The presence of multiple electrons in an atom leads to a phenomenon known as the screening effect or shielding effect. Electrons in inner energy levels shield the outer electrons from the full attractive force of the nucleus. As a result, the effective nuclear charge experienced by the outer electrons is reduced. The Bohr model does not consider this screening effect, which affects the energy levels of the electrons in multi-electron atoms.

4. Coulomb's law no longer valid:
Coulomb's law describes the force between two charged particles, such as the force of attraction between the nucleus and an electron. However, in multi-electron atoms, the presence of multiple electrons introduces complexities that go beyond the simple application of Coulomb's law. The repulsion between electrons and the shielding effect make the force between the nucleus and an electron more intricate than what can be described by Coulomb's law alone.

Conclusion:
In conclusion, the simple Bohr model cannot be directly applied to calculate the energy levels of atoms with many electrons due to the electron not being subject to a central force, electron-electron collisions, the screening effect, and the inadequacy of Coulomb's law to fully describe the interactions in multi-electron atoms. These factors necessitate the use of more advanced quantum mechanical models to accurately determine the energy levels and behavior of electrons in complex atomic systems.