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.