QJEEAdv24Ch2ff1: JEE Advanced 2024 Chemistry - Class 11 JEEAdv24Ch2ff1 Solution: Among the following, the correct statement(s) for electrons in…

Let's analyze each statement one by one:

Option A: Uncertainty principle rules out the existence of definite paths for electrons.

This statement is correct. The Heisenberg Uncertainty Principle states that it is impossible to simultaneously know both the exact momentum and the exact position of a particle. Therefore, the concept of a definite path for electrons is not applicable according to quantum mechanics.

Option B: The energy of an electron in $$2s$$ orbital of an atom is lower than the energy of an electron that is infinitely far away from the nucleus.

This statement is also correct. The energy of an electron in any bound state (such as the $$2s$$ orbital) is always lower (more negative) than that of an electron at an infinite distance from the nucleus (which would have zero energy). This is because an electron infinitely far away from the nucleus is considered to be free from nuclear attraction and thus its potential energy is zero.

Option C: According to Bohr's model, the most negative energy value for an electron is given by $$n=1$$, which corresponds to the most stable orbit.

This statement is correct as well. In Bohr’s model of the atom, the energy levels of electrons are given by $$E_n=-\frac{13.6eV}{n^2}$$. The energy is most negative when $$n=1$$, indicating the most stable orbit and thus the lowest energy state (the ground state).

Option D: According to Bohr's model, the magnitude of velocity of electrons increases with increase in values of $$n$$.

This statement is incorrect. According to Bohr’s model, the speed of an electron in a circular orbit around the nucleus decreases with an increase in the principal quantum number $$n$$. The velocity $$v_n$$ is given by the formula: $$v_n=\frac{2.18\times {10}^{6}m/s}{n}$$, where $$n$$ is the principal quantum number. Hence, as $$n$$ increases, $$v_n$$ decreases.

Therefore, the correct statements are:

Option A, Option B, and Option C.