What could the fourth quantum number of a $3 p^3$ electron be?
A. $m_s=+1$
B. $m_s=0$
C. $m_s=-\frac{1}{2}$
D. $m_s=-1
Answer (2)
The fourth quantum number of an electron in a 3 p 3 configuration can only be either + 2 1 or − 2 1 . Among the provided options, C ( m s = − 2 1 ) is valid. The other options do not represent possible values for the spin quantum number.
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The spin quantum number ( m s ) describes the intrinsic angular momentum of an electron.
m s can only have two possible values: + 2 1 (spin up) and − 2 1 (spin down).
Options A ( m s = + 1 ), B ( m s = 0 ), and D ( m s = − 1 ) are not valid values for m s .
The correct answer is C ( m s = − 2 1 ). − 2 1
Explanation
Understanding the Problem The question asks about the possible values of the fourth quantum number, m s , of an electron in a 3 p 3 configuration. This quantum number is also known as the spin quantum number.
Possible Values of Spin Quantum Number The spin quantum number, m s , describes the intrinsic angular momentum of an electron, which is quantized and referred to as spin. It can only have two possible values: spin up ( + 2 1 ) or spin down ( − 2 1 ).
Analyzing the Options Now, let's examine the given options:
A. m s = + 1 - This is not a possible value for the spin quantum number.
B. m s = 0 - This is also not a possible value for the spin quantum number.
C. m s = − 2 1 - This is a possible value for the spin quantum number (spin down).
D. m s = − 1 - This is not a possible value for the spin quantum number.
Final Answer Therefore, the correct answer is C, as it is the only option that represents a valid value for the spin quantum number m s .
Examples
Understanding quantum numbers is crucial in fields like material science and quantum computing. For instance, when designing new materials with specific magnetic properties, knowing the possible spin states of electrons helps predict the material's overall behavior. Similarly, in quantum computing, electron spin is used to represent quantum bits (qubits), and controlling these spin states is essential for performing quantum computations. The spin quantum number is also important in understanding atomic spectroscopy, where transitions between different spin states can lead to the emission or absorption of light at specific wavelengths.
