Question

An electron in its ground state has the following set of quantum numbers: {n=1, ℓ=0, mₗ=0, mₛ=+1/2}. Upon excitation by light, which state would it transition to?

a) {n=1, ℓ=0, m_s=0, m_s=+1/2}
b) {n=1, ℓ=0, m_s=0, m_s=-1/2}
c) {n=2, ℓ=0, m_s=0, m_s=-1/2}
d) {n=2, ℓ=0, m_s=0, m_s=+1/2}

Answer 1

An excited electron transitions to a higher energy state, affecting its principal quantum number (n) while leaving its spin quantum number (ms) unchanged. The correct transition state for the given electron's ground state quantum numbers would be option (d) with quantum numbers {n=2, ℓ=0, mₙ=0, mₛ=+1/2}.

Step-by-step explanation:

When an electron in its ground state is excited by light, it transitions to a higher energy state by absorbing a specific amount of energy defined by the difference in energy between the higher and the ground state.

This transition changes the principal quantum number (n) of the electron, since the principal quantum number defines the energy level.

The correct transition would leave the spin quantum number (ms) unchanged, as the spin does not depend on the excitation by light.

From the given options, the electron in its ground state with quantum numbers {n=1, ℓ=0, mₙ=0, mₛ=+1/2} would transition to a state where the principal quantum number has increased, hence the new state would be with {n=2, ℓ=0, mₙ=0, mₛ=+1/2}.

The correct choice among the provided options that reflects such a transition is (d).

Remember that the quantum numbers define distinct states for an electron in an atom, and no two electrons can occupy the same quantum state simultaneously—a principle known as the Pauli exclusion principle