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Answer :
Sure! Let's determine the quantum numbers [tex]\( n \)[/tex] and [tex]\( \ell \)[/tex], and identify all possible values for [tex]\( m_{\ell} \)[/tex] for the subshell 4s.
1. Principal Quantum Number [tex]\( n \)[/tex]:
The principal quantum number [tex]\( n \)[/tex] specifies the energy level and distance of the electron from the nucleus. For the subshell 4s, the principal quantum number [tex]\( n \)[/tex] is 4.
2. Azimuthal Quantum Number [tex]\( \ell \)[/tex]:
The azimuthal quantum number [tex]\( \ell \)[/tex] determines the shape of the orbital and can take values from 0 to [tex]\( n-1 \)[/tex]. The letter designation of the subshell (s, p, d, f) corresponds to specific values of [tex]\( \ell \)[/tex]:
- s corresponds to [tex]\( \ell = 0 \)[/tex]
- p corresponds to [tex]\( \ell = 1 \)[/tex]
- d corresponds to [tex]\( \ell = 2 \)[/tex]
- f corresponds to [tex]\( \ell = 3 \)[/tex]
For an s orbital (like 4s), [tex]\( \ell \)[/tex] is 0.
3. Magnetic Quantum Number [tex]\( m_{\ell} \)[/tex]:
The magnetic quantum number [tex]\( m_{\ell} \)[/tex] determines the orientation of the orbital in space. It can take integer values from [tex]\(-\ell\)[/tex] to [tex]\(+\ell\)[/tex], including zero. For [tex]\( \ell = 0 \)[/tex], the only value for [tex]\( m_{\ell} \)[/tex] is 0.
Thus, for the 4s subshell:
- The principal quantum number [tex]\( n \)[/tex] is 4.
- The azimuthal quantum number [tex]\( \ell \)[/tex] is 0.
- The possible value for the magnetic quantum number [tex]\( m_{\ell} \)[/tex] is 0.
So, for the element 4s:
- [tex]\( n = 4 \)[/tex]
- [tex]\( \ell = 0 \)[/tex]
- The possible value for [tex]\( m_{\ell} = 0 \)[/tex]
These are the quantum numbers and the possible value of [tex]\( m_{\ell} \)[/tex] for the 4s subshell.
1. Principal Quantum Number [tex]\( n \)[/tex]:
The principal quantum number [tex]\( n \)[/tex] specifies the energy level and distance of the electron from the nucleus. For the subshell 4s, the principal quantum number [tex]\( n \)[/tex] is 4.
2. Azimuthal Quantum Number [tex]\( \ell \)[/tex]:
The azimuthal quantum number [tex]\( \ell \)[/tex] determines the shape of the orbital and can take values from 0 to [tex]\( n-1 \)[/tex]. The letter designation of the subshell (s, p, d, f) corresponds to specific values of [tex]\( \ell \)[/tex]:
- s corresponds to [tex]\( \ell = 0 \)[/tex]
- p corresponds to [tex]\( \ell = 1 \)[/tex]
- d corresponds to [tex]\( \ell = 2 \)[/tex]
- f corresponds to [tex]\( \ell = 3 \)[/tex]
For an s orbital (like 4s), [tex]\( \ell \)[/tex] is 0.
3. Magnetic Quantum Number [tex]\( m_{\ell} \)[/tex]:
The magnetic quantum number [tex]\( m_{\ell} \)[/tex] determines the orientation of the orbital in space. It can take integer values from [tex]\(-\ell\)[/tex] to [tex]\(+\ell\)[/tex], including zero. For [tex]\( \ell = 0 \)[/tex], the only value for [tex]\( m_{\ell} \)[/tex] is 0.
Thus, for the 4s subshell:
- The principal quantum number [tex]\( n \)[/tex] is 4.
- The azimuthal quantum number [tex]\( \ell \)[/tex] is 0.
- The possible value for the magnetic quantum number [tex]\( m_{\ell} \)[/tex] is 0.
So, for the element 4s:
- [tex]\( n = 4 \)[/tex]
- [tex]\( \ell = 0 \)[/tex]
- The possible value for [tex]\( m_{\ell} = 0 \)[/tex]
These are the quantum numbers and the possible value of [tex]\( m_{\ell} \)[/tex] for the 4s subshell.
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