Which of the following statements does not form a part of Bohrs model of hydrogen atom?

The correct option is: "The position and velocity of the electrons in the orbit cannot be determined simultaneously"

To understand why this statement is not a part of Bohr's model of the hydrogen atom, let us break down the postulates of Bohr's model and compare them with the principles of quantum mechanics.

1. Postulates of Bohr's Model:
Niels Bohr introduced his model of the atom in 1913. The main postulates include:
• Electrons revolve in specific circular orbits: Electrons revolve around the nucleus only in certain selected circular paths called stationary orbits. This aligns with the option: "Electrons revolve in different orbits around the nucleus".
• Energy is quantized: The energy of an electron in a given orbit is constant and restricted to certain discrete values. It can only change by moving from one discrete energy level to another. This matches the option: "Energy of the electrons in the orbit is quantised".
• Lowest energy state: The orbit closest to the nucleus has the lowest energy level (ground state, where $n=1$). As we move outward to orbits with higher quantum numbers, the energy increases. This supports the option: "The electron in the orbit nearest the nucleus has the lowest energy".
• Fixed position and path: In Bohr's model, the electron is treated as a particle moving in a well-defined circular path (orbit) with a precisely known radius and velocity at any given instant.

2. The Heisenberg Uncertainty Principle:
The statement "The position and velocity of the electrons in the orbit cannot be determined simultaneously" is the definition of the Heisenberg Uncertainty Principle, which was formulated by Werner Heisenberg in 1927.
Mathematically, the uncertainty principle is expressed as:

$\Delta x·\Delta p\ge \frac{h}{4\pi }$

where $\Delta x$ is the uncertainty in position, $\Delta p$ (or $m\Delta v$) is the uncertainty in momentum/velocity, and $h$ is Planck's constant.

3. Conclusion:
Because Bohr's model assumes that electrons move in well-defined circular orbits with precise positions and velocities, it directly contradicts Heisenberg's Uncertainty Principle. The uncertainty principle was proposed later and is a cornerstone of modern quantum mechanics (the wave mechanical model), not Bohr's semi-classical model.
Therefore, the statement regarding the inability to simultaneously determine the position and velocity of an electron is not a part of Bohr's model.