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Quantum numbers are used to uniquely identify an electron in an atom. The Pauli exclusion principle...

Quantum numbers are used to uniquely identify an electron in an atom. The Pauli exclusion principle states that no two electrons in an atom may have the same set of four quantum numbers

List a possible set of four quantum numbers (n,l ,ml ,ms ) in order, for the highest energy electron in gallium, . Refer to the periodic table as necessary.

Enter four numbers separated by commas (e.g., 3,2,-2,1/2).
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Concepts and reason

The concept used is to identify the valid set of quantum numbers for the highest energy electrons in Gallium.

Fundamentals

The electrons in an atom are filled in the order of increasing energy of orbitals.

The increasing order of the energy of orbitals is as follows:

1s 2s 2p 3s 3p < 4s <3d <4p < 5s < 4d <5p < 6s <45 < 5 < 6p...

The four quantum numbers required to describe an atom are principal quantum number, azimuthal quantum number, magnetic quantum number and spin quantum number.

Principal quantum number: It describes the energy level of an electron. It is denoted by n. The value of n ranges from 1 to the level of the electron in the outermost orbit.

Azimuthal quantum number: It describes the sub-shell of an electron. It is denoted by l.

The value of l ranges from 0 to (n-1)
.

Magnetic quantum number: It describes the energy levels of the sub-shell of an electron. It is denoted by .

The value of ranges from to .

Spin quantum number: It describes the spin of an electron. It is denoted by .

The value of can either be or .

According to Pauli’s exclusion principle, no two electrons can have same four quantum numbers.

The atomic number of Gallium is .

The ground state electronic configuration of Gallium is as follows:

Ga – 31-[Ar]3d 4s²4 p

The electron may occupy , or orbital.

The spin of the electron may be % - 10%+
.

Hence, there are (2x 3) = 6
possible sets of quantum numbers for the highest energy electron in Gallium.

For a electron, and

So, for a electron may be -1, 0, +1
.

for a electron may be % - 10%+
.

The 6 possible sets of quantum numbers for the highest energy electron in Gallium are as follows:

+1=
4,1 -1-5
4,10+5
4,10-
4,1 ++ 5
=+ነን

Ans:

The possible sets of quantum numbers for the highest energy electron in Gallium are as follows:

+1=
4,1 -1-5
4,10+5
4,10-
4,1 ++ 5
=+ነን

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