Chemistry - Atomic Structure Question with Solution | TestHub

The given quantum numbers are $l=1$, $m=0$, $m_s=+\frac{1}{2}$.

For $l=1$, the minimum principal quantum number $n$ is 2.

This set of quantum numbers describes a specific electron state.

According to the Pauli Exclusion Principle, no two electrons in an atom can have the exact same set of four quantum numbers. However, another electron could have $m_s=-\frac{1}{2}$ with the same $n$, $l$, and $m$ values.

A. Incorrect. For $l=1$, the electron is in a p subshell, which first appears in the L shell ($n=2$). The K shell only has $n=1$, so $l=0$.

B. Incorrect. A double dumbbell shape describes a d orbital ($l=2$). For $l=1$, the orbital is dumbbell-shaped (p orbital).

C. Incorrect. For $l=1$, the least possible principal quantum number $n$ is 2, not 3.

D. Correct. Another electron can have the same $n$, $l$, and $m$ values but with $m_s=-\frac{1}{2}$. This is allowed by the Pauli Exclusion Principle.

Final Answer: The final answer is D