Answer :
Final answer:
In both a hydrogen atom and a helium ion in the second excited state, the angular momentum of the electrons can be the same, leading to l1 being equal to l2. The correct answer is a) l1 = l2
Explanation:
The angular momentum of an electron in a hydrogen-like atom in a quantum state is given by the formula L = √(l(l+1))ħ, where ħ is the reduced Planck's constant and l is the angular momentum quantum number.
In a given quantum state, both hydrogen and helium ions (assuming the helium ion has a single electron, like hydrogen) have the same principal quantum number n and can have the same l values.
Therefore, both a hydrogen atom and a helium ion in the same excited state (second excited state implies n = 3) will have electrons that have the same possible l values, and hence the same possible angular momenta.
Given the two states have electrons with the same l, we conclude that the angular momentum for both, denoted l1 and l2 respectively, will be equal, assuming they are in the same l substate. Hence, the correct answer is l1 = l2.
