Which statement is true when the principal quantum number n equals 1 for an electron in an atom?

• A. The electron is in the lowest energy level, also known as the ground state.
• B. The electron can have an angular momentum quantum number l equal to 1.
• C. The electron is found in the p orbital.
• D. The electron can have a magnetic quantum number m_l equal to 2.

Answer: (A)

Verified step by step guidance

1. Recall that the principal quantum number \(n\) determines the main energy level or shell of an electron in an atom. When \(n = 1\), the electron is in the first and lowest energy level, often called the ground state.
2. Understand that the angular momentum quantum number \(l\) can take integer values from \$0\( up to \)n-1\(. For \)n = 1\(, this means \)l\( can only be \)0$.
3. Recognize that the value of \(l\) corresponds to the type of orbital: \(l = 0\) is an s orbital, \(l = 1\) is a p orbital, \(l = 2\) is a d orbital, and so on. Since \(l\) must be \$0\( when \)n = 1$, the electron cannot be in a p orbital.
4. The magnetic quantum number \(m_l\) depends on \(l\) and can take values from \(-l\) to \(+l\). For \(l = 0\), \(m_l\) can only be \$0\(, so \)m_l = 2\( is not possible when \)n = 1$.
5. Therefore, the only true statement when \(n = 1\) is that the electron is in the lowest energy level, the ground state.