Answer :
Since l can be 0,1,2... up to n-1 and m can be -l, -l+1... up to l, I say this
l=0, m=2, m=-2. It's worth saying that these equalities can not be simultaneous, but they are possible for the shell n=3 separately
l=0, m=2, m=-2. It's worth saying that these equalities can not be simultaneous, but they are possible for the shell n=3 separately
Answer : The correct options are, [tex]l=0,m=-2\text{ and }m=2[/tex]
Explanation :
Principle Quantum Numbers : It describes the size of the orbital and the energy level. It is represented by n. Where, n = 1,2,3,4....
Azimuthal Quantum Number : It describes the shape of the orbital. It is represented as 'l'. The value of l ranges from 0 to (n-1). For l = 0,1,2,3... the orbitals are s, p, d, f...
Magnetic Quantum Number : It describes the orientation of the orbitals. It is represented as [tex]m_l[/tex]. The value of this quantum number ranges from [tex](-l\text{ to }+l)[/tex]. When l = 2, the value of [tex]m_l[/tex] will be -2, -1, 0, +1, +2.
Spin Quantum number : It describes the direction of electron spin. This is represented as [tex]m_s[/tex] The value of this is [tex]+\frac{1}{2}[/tex] for upward spin and [tex]-\frac{1}{2}[/tex] for downward spin.
As we are given that, [tex]n=3[/tex]
So,
[tex]l=0,1,2[/tex]
[tex]m_l=-2,-1,0,1,2[/tex]
[tex]m_s=+\frac{1}{2}\text{ and }-\frac{1}{2}[/tex] (For each sub-shell)
Hence, from this we conclude that, the valid quantum numbers are [tex]l=0,m=-2\text{ and }m=2[/tex]