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The quantum numbers of six elements are ...

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):}`

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To arrange the quantum numbers of the six elements in order of increasing energies, we will use the n + l rule. According to this rule, the energy of an electron in an atom is determined by the sum of the principal quantum number (n) and the azimuthal quantum number (l). The lower the value of n + l, the lower the energy. If two electrons have the same n + l value, the one with the lower n value has lower energy. Let's analyze the quantum numbers provided: 1. **(1)** n = 4, l = 2 → n + l = 4 + 2 = 6 2. **(2)** n = 3, l = 2 → n + l = 3 + 2 = 5 3. **(3)** n = 4, l = 1 → n + l = 4 + 1 = 5 4. **(4)** n = 3, l = 2 → n + l = 3 + 2 = 5 ...
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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):}

The quantum numbers of six electrons are given below. Arrange them in order of increasing energies. If any of these combination(s) has/have the same energy lists: 1. n=4 , l=2 , m_(i) =-2, m_(s) =-1//2 2. n=3 , l=2 , m_(l) =1 , m_(s) =+1//2 3. n=4 , l=2 ,m_(l)=-2, m_(s) =-1//2 4. n=3 , l= 2, m_(i) =-1 , 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

The quantum number of electrons are given below: Arrange then in order of increasing energies a. n= 4,l= 2,m_(1)= -2, m_(s)= -(1)/(2) b. n= 3,l= 2,m_(1) = 1, m_(s)= +(1)/(2) c. n= 4,l= 1,m_(1) = 0, m_(s)= +(1)/(2) e.n= 3,l= 2,m_(1)= -2, m_(s)= +(1)/(2) f. n= 4,l= 1,m_(1) = +1, m_(s)= +(1)/(2)

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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

How many electrons in a given atom can have the following quantum numbers ? (a) n = 3, l = 1 (b) n = 3, l = 2, m_l = 0 (c ) n = 3, l = 2, m_l = +2, m_s = + 1/2 (d) n = 3 .

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Describe the orbital with the following quantum numbers : (i) n = 1, l = 0 " " (ii) n = 2, l = 1, m = 0 (iii) n = 3, l = 2 " " (iv) n = 4, l = 1 (v) n = 3, l = 0, m = 0 " " (vi) n = 3, l = 1 .