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Explain given reasons, which of the foll...

Explain given reasons, which of the following sets of quantum numbers are not possible.
`{:((a) n = 0 ",", l = 0",", m_l=0",", m_s = + 1//2),((b) n = 1 ",", l = 0",", m_l=0",", m_s = - 1//2),((c) n = 1 ",", l = 1",", m_l=-0",", m_s = + 1//2),((d) n = 2 ",", l = 1",", m_l=0",", m_s = - 1//2),((e) n = 3 ",", l = 3",", m_l=-3",", m_s = + 1//2),((f) n = 3 ",", l = 2",", m_l=0",", m_s = + 1//2):}`

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To determine which sets of quantum numbers are not possible, we need to apply the rules governing quantum numbers: 1. **Principal Quantum Number (n)**: This can take positive integer values (n = 1, 2, 3,...). The smallest value of n is 1. 2. **Azimuthal Quantum Number (l)**: This can take values from 0 to (n-1). Therefore, for a given n, l can be 0, 1, 2,... up to (n-1). 3. **Magnetic Quantum Number (m_l)**: This can take values from -l to +l, including 0. 4. **Spin Quantum Number (m_s)**: This can be either +1/2 or -1/2. Now, let's analyze each set of quantum numbers: ...
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The quantum numbers of six elements are given below. Arrange them in order of increasing energies. If any of these combinations has/have the same energies, list them. {:((1) n = 4 ",", l = 2",", m_l=-2",", m_s = - 1/2),((2) n = 3 ",", l = 2",", m_l=0",", m_s = + 1/2),((3) n = 4 ",", l = 1",", m_l= 0",", m_s = + 1/2),((4) n = 3 ",", l = 2",", m_l=-2",", m_s = - 1/2),((5) n = 3 ",", l = 1",", m_l=-1",", m_s = + 1/2),((6) n = 4 ",", l = 1",", m_l=0",", m_s = + 1/2):}

Explain , giving reason , which of the following sets of quantum number are not possible {:(a,n= 0 ,l = 0, m_(1) = 0, m_(s) = +1//2),(b,n= 1 ,l = 0, m_(1) = 0, m_(s) = -1//2),(c,n= 1 ,l = 0, m_(1) = 0, m_(s) = +1//2),(d,n= 2 ,l = 1, m_(1) = 0, m_(s) = -1//2),(e,n= 3 ,l = 3, m_(1) = -3, m_(s) = +1//2),(f,n= 3 ,l = 1, m_(1) = 0, m_(s) = +1//2):}

Which of the following sate of quantum numbers is not permissible for an electron in an atom? (i) n = 1,l = 1, m_(l) 0, m_(s) =+ 1//2 (ii) n = 3, l = 1, m_(1) =- 2, m_(s) =- 1//2 (iii) n =1, l = 1, m_(l) = 0, m_(s) =+ 1//2 (iv) n = 2, l = 0, m_(l) = 0, m_(s) = 1

Which of the following set of quantum numbers are not permited (a) n=3, l=2,m=-2,s=+1/2 (b) n=3, l=2, m=-1,s=0 (c) n=2 ,l=2,m=+1,s=-1/2

From the following sets of quantum numbers , state which are possible ? (i) n=0,l=0,m_(l)=1,m_(s)= +1//2 (ii) n=2,l=1,m_(l)=0,m_(s) = -1//2 (iii) n=2, l=0,m_(1)=3,m_(s) = +1//2 (iv) n=3,l=1,m_(l)=0,m_(s) = +1//2

From the following sets quantum number state which are possible. Explain why the other are not permitted ? a. n = 0, l = 0, m= 0, s = + 1//2 b. n = 1, l = 0, m= 0, s = - 1//2 c. n = 1, l = 1, m= 0, s = + 1//2 d. n = 1, l = 0, m= +1, s = + 1//2 e. n = 0, l = 1, m= -1, s = - 1//2 f. n = 2, l = 2, m= 0, s = - 1//2 g. n = 2, l = 1, m= 0, s = - 1//2

From the following sets of quantum numbers, state which are possible. Explain why the others are not possible. (a) n=0, l=0, m_(l)=0, s=+1//2 , (ii) n=1, l=0, m_(l)=0, s=-1//2 (iii) n=1, l=1, m_(1)=0, s=+1//2 , (iv) n=1, l=0, m_(l)=+1, s=+1//2