What is the third quantum number of a $3 s^2$ electron in phosphorus, $1 s^2 2 s^2 2 p^6 3 s^2 3 p^3$?
A. $m_l=0$
B. $m_l=2$
C. $m_l=1$
D. $m_l=3
Answer (2)
The magnetic quantum number m l for a 3 s 2 electron in phosphorus is 0, which is the only value possible for an s subshell. Therefore, the correct answer is A. m l = 0 .
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Identify the principal quantum number (n) and the azimuthal quantum number (l) for a 3s electron.
Determine the possible values of the magnetic quantum number ( m l ) based on the value of l.
Since l = 0, m l can only be 0.
The third quantum number of a 3 s 2 electron in phosphorus is 0 .
Explanation
Understanding the Problem The question asks for the third quantum number, m l , of a 3 s 2 electron in phosphorus, given its electron configuration 1 s 2 2 s 2 2 p 6 3 s 2 3 p 3 . We need to determine the value of m l for a 3 s electron.
Identifying Quantum Numbers For a 3 s electron, the principal quantum number n = 3 , and the azimuthal quantum number l = 0 . The magnetic quantum number, m l , can take values from − l to + l , including 0.
Determining the Value of m_l Since l = 0 , the only possible value for m l is 0. Therefore, the third quantum number of a 3 s 2 electron in phosphorus is m l = 0 .
Final Answer The correct answer is A. m l = 0 .
Examples
Understanding quantum numbers is crucial in fields like material science and quantum computing. For instance, knowing the magnetic quantum number helps predict how electrons in a material will behave under a magnetic field, which is essential for designing new magnetic storage devices or understanding the properties of semiconductors. The quantum numbers define the state of an electron and dictate its behavior in atoms and molecules, enabling us to engineer materials with specific properties.
