In an atom which has 2k , 8L ,18M and 2N electrons present in the grou...
In an atom which has 2k , 8L ,18M and 2N electrons present in the grou...
**Number of Electrons Present in m=0**
In order to determine the number of electrons present in the m=0 state in an atom with 2k, 8L, 18M, and 2N electrons in the ground state, we need to understand the quantum numbers and their relationship to electron distribution.
**Quantum Numbers:**
Quantum numbers are used to describe the energy levels and spatial distribution of electrons in an atom. They include:
1. Principal Quantum Number (n): Determines the energy level or shell in which an electron resides. It can have integer values starting from 1.
2. Azimuthal Quantum Number (l): Defines the subshell or orbital in which an electron is found. It can have values ranging from 0 to n-1.
3. Magnetic Quantum Number (m): Specifies the orientation of the orbital in space. It can have values ranging from -l to +l.
4. Spin Quantum Number (s): Represents the spin of an electron, either +1/2 or -1/2.
**Electron Distribution:**
The electron distribution in an atom follows specific rules based on the quantum numbers and the Pauli exclusion principle which states that no two electrons in an atom can have the same set of four quantum numbers.
For the given atom with 2k, 8L, 18M, and 2N electrons in the ground state, we can determine the number of electrons present in the m=0 state by considering the values of the azimuthal quantum number (l) for each subshell.
- 2k electrons: These electrons are present in the 1s subshell, where l=0. Since l=0, the magnetic quantum number (m) can only be 0. Therefore, all 2k electrons will have m=0.
- 8L electrons: These electrons are present in the 2s and 2p subshells. For the 2s subshell, l=0 and m=0. Therefore, all 2 electrons in the 2s subshell will have m=0. For the 2p subshell, l=1 and the possible values of m are -1, 0, and 1. However, since we are only interested in m=0, none of the 6 electrons in the 2p subshell will have m=0.
- 18M electrons: These electrons are present in the 3s, 3p, and 3d subshells. Similar to the previous cases, for the 3s subshell (l=0), all 2 electrons will have m=0. For the 3p subshell (l=1), none of the 6 electrons will have m=0 since the only possible values of m are -1, 0, and 1. However, for the 3d subshell (l=2), the possible values of m are -2, -1, 0, 1, and 2. Among these, only the 10 electrons in the 3d subshell with m=0 will contribute to the m=0 state.
- 2N electrons: These electrons are present in the 4s subshell (l=0). Therefore, all 2 electrons in the 4s subshell will have m=0.
**Summary:**
Based on the distribution
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