In the Bohr model of the hydrogen atom, electrons are assumed to orbit the nucleus in discrete energy levels. According to classical physics, when an object moves in a circular path, it possesses angular momentum. In the Bohr model, the electron in the ground state is considered to be in a stable, lowest-energy orbit and has non-zero orbital angular momentum.
However, in quantum mechanics, the behavior of particles is described by wave functions and probabilities rather than classical trajectories. The angular momentum of a particle in quantum mechanics is quantized, meaning it can only take on certain discrete values. The orbital angular momentum of an electron in the hydrogen atom is given by the quantum number ℓ, and it is quantized according to the equation:
L = ħ√(ℓ(ℓ + 1))
Where L is the orbital angular momentum, ℓ is the quantum number, and ħ (h-bar) is the reduced Planck's constant.
In the ground state of the hydrogen atom (n = 1, where n is the principal quantum number), the quantum number ℓ takes the value of 0. This means that the orbital angular momentum of the electron in the ground state is zero. It is important to note that even though the electron does not possess orbital angular momentum in this state, it still possesses intrinsic angular momentum or spin, which is a distinct property in quantum mechanics.
So, the apparent discrepancy between the Bohr model and quantum mechanics regarding the angular momentum of the electron in the hydrogen atom's ground state is resolved by recognizing that the Bohr model is an approximation that does not fully capture the quantum mechanical nature of the system. Quantum mechanics provides a more accurate description of the behavior of particles at the atomic scale, where properties such as angular momentum are quantized.