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The position and energy of an electron i...

The position and energy of an electron is specified with the help of four quantum numbers namely, principal quantum number (n), azimuthal quantum number (l), magnetic quantum number `(m_l)` and spin quantum number `(m_s)` . The permissible values of these are :
`n = 1,2.....`
`l = 0,1,.....(n-1)`
`m_l = -l,......0,......+l`
`m_s = +1/2 and -1/2` for each value of `m_l`.
The angular momentum of electron is given as `sqrt(l(l + 1)) cdot h/(2pi)`
While spin angular momentum is given as `sqrt(s(s+1)) cdot (h/(2pi))` where `s = 1/2`
The electrons having the same value of `n, l and m_l` are said to belong to the same orbital. According to Pauli's exclusion principle, an orbital can have maximum of two electrons and these two must have opposite spin.
Which of the following statements is not correct ?

A

For sodium, the outermost electron has `n = 3, l = 0 , m_l = 0, s = +1//2`

B

The orbitals having `n = 3, l = 2, m_l = -2` have same energies

C

For 4f electron, `n =4, l = 3, m_l = 0, s = +1//2` is not possible.

D

The orbital 2d, 3f and 4g are not possible.

Text Solution

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The correct Answer is:
To determine which statement is not correct regarding quantum numbers and electron configurations, we will analyze each statement based on the rules of quantum mechanics. ### Step-by-Step Solution: 1. **Understanding Quantum Numbers**: - The four quantum numbers are: - Principal quantum number (n): Indicates the energy level. - Azimuthal quantum number (l): Indicates the subshell (s, p, d, f). - Magnetic quantum number (m_l): Indicates the orientation of the orbital. - Spin quantum number (m_s): Indicates the spin of the electron. 2. **Analyzing Each Statement**: - **Statement 1**: "For sodium, the outermost electron has n=3, l=0, m_l=0, m_s=+1/2." - Sodium (Na) has an atomic number of 11. Its electron configuration is 1s² 2s² 2p⁶ 3s¹. - The outermost electron is indeed in the 3s subshell, which corresponds to n=3, l=0 (s subshell), m_l=0, and m_s can be +1/2 or -1/2. This statement is correct. - **Statement 2**: "The orbital having n=3, l=2, m_l=-2 have same energies." - For n=3, l can take values 0, 1, or 2. The l=2 corresponds to the d subshell. The magnetic quantum number m_l can range from -2 to +2, giving five possible values (-2, -1, 0, +1, +2). All d orbitals in the same energy level (n=3) are degenerate (same energy). This statement is correct. - **Statement 3**: "For 4f electron, n=4, l=3, m_l=0 is not possible." - For 4f, n=4 and l=3 is correct (f subshell). The magnetic quantum number m_l can range from -3 to +3, which includes 0. Thus, m_l=0 is indeed possible. This statement is incorrect. - **Statement 4**: "The orbitals 2d, 3f, and 4g are not possible." - The 2d orbital is not possible since for n=2, l can only be 0 (s) or 1 (p). The 3f orbital is not possible since for n=3, l can only be 0 (s), 1 (p), or 2 (d). The 4g orbital is also not possible since for n=4, l can only be 0 (s), 1 (p), 2 (d), or 3 (f). This statement is correct. 3. **Conclusion**: - The statement that is not correct is **Statement 3**: "For 4f electron, n=4, l=3, m_l=0 is not possible."

To determine which statement is not correct regarding quantum numbers and electron configurations, we will analyze each statement based on the rules of quantum mechanics. ### Step-by-Step Solution: 1. **Understanding Quantum Numbers**: - The four quantum numbers are: - Principal quantum number (n): Indicates the energy level. - Azimuthal quantum number (l): Indicates the subshell (s, p, d, f). ...
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Knowledge Check

  • The position and energy of an electron is specified with the help of four quantum numbers namely, principal quantum number (n), azimuthal quantum number (l), magnetic quantum number (m_l) and spin quantum number (m_s) . The permissible values of these are : n = 1,2..... l = 0,1,.....(n-1) m_l = -l,......0,......+l m_s = +1/2 and -1/2 for each value of m_l . The angular momentum of electron is given as sqrt(l(l + 1)) cdot h/(2pi) While spin angular momentum is given as sqrt(s(s+1)) cdot (h/(2pi)) where s = 1/2 The electrons having the same value of n, l and m_l are said to belong to the same orbital. According to Pauli's exclusion principle, an orbital can have maximum of two electrons and these two must have opposite spin. The maximum number of electrons having n + l = 5 in an atom is

    A
    32
    B
    18
    C
    10
    D
    8
  • The position and energy of an electron is specified with the help of four quantum numbers namely, principal quantum number (n), azimuthal quantum number (l), magnetic quantum number (m_l) and spin quantum number (m_s) . The permissible values of these are : n = 1,2..... l = 0,1,.....(n-1) m_l = -l,......0,......+l m_s = +1/2 and -1/2 for each value of m_l . The angular momentum of electron is given as sqrt(l(l + 1)) cdot h/(2pi) While spin angular momentum is given as sqrt(s(s+1)) cdot (h/(2pi)) where s = 1/2 The electrons having the same value of n, l and m_l are said to belong to the same orbital. According to Pauli's exclusion principle, an orbital can have maximum of two electrons and these two must have opposite spin. For an electron having n = 3 and l = 0 , the orbital angular momentum is

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    `((sqrt3)h)/(pi)`
    B
    `sqrt(6) h/(2pi)`
    C
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    D
    `2sqrt(3) h/pi`
  • If m = magnetic quantum number and l = azimuthal quantum number then :-

    A
    `m=l+2`
    B
    `m=2l^(2)+1`
    C
    `l=(m-1)/(2)`
    D
    `l=2m+1`
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