Question

given n = 2, identify which of the quantum numbers is not possible. answer: a l = 1 b l = 2 c m_l=-1 d m_s=+\frac{1}{2} e m_s=-\frac{1}{2}

Explanation:

Step1: Recall quantum - number rules

The principal quantum number $n$ determines the possible values of the angular - momentum quantum number $l$, magnetic quantum number $m_l$, and spin quantum number $m_s$. The allowed values of $l$ range from $0$ to $n - 1$. When $n=2$, $l$ can be $0$ or $1$. The values of $m_l$ range from $-l$ to $+l$. The spin quantum number $m_s$ can be either $+\frac{1}{2}$ or $-\frac{1}{2}$.

Step2: Analyze each option

• Option A: When $n = 2$, $l$ can be $1$ since $l$ ranges from $0$ to $n - 1$ ($0$ and $1$ for $n = 2$).
• Option B: When $n=2$, $l$ cannot be $2$ because $l$ ranges from $0$ to $n - 1$, and $n-1=1$ for $n = 2$.
• Option C: If $l = 1$, $m_l$ can be $- 1$ (since $m_l$ ranges from $-l$ to $+l$ and when $l = 1$, $m_l=-1,0,1$).
• Option D: $m_s=+\frac{1}{2}$ is a valid spin - quantum number value.
• Option E: $m_s=-\frac{1}{2}$ is a valid spin - quantum number value.

Answer:

B. $l = 2$