4. (12 pts) Explain why a fourth quantum number that describes the spin of elect

Question

4. (12 pts) Explain why a fourth quantum number that describes the spin of electrons is required to describe the properties of electrons in atoms and ions a. Describe the characteristics (shapes) of the four ground state orbitals. of the following orbitals do not exist: 1p, 2s, 2d, 3p, 3d, 3f, 4g Which b. c. Indicate which of the following sets of quantum numbers in an atom are unacceptable and explain why (3,0,0,%) 5. (10 pts.) a. What is an electron configuration? Describe the roles the Pauli Exclusion Principle and Hund's Rule play in writing the electron configurations of elements

Explanation / Answer

Q4:

(a) Electron has an intrinsic spin. The corresponding spin angular momentum can take two directions. These two directions of spin angular momentum correspond to two spin energy states. Spin quantum number is used to designate these spin energy states.

(b) TThe shape of s is sperical

Shape of p-orbital is dumbel. It has two lobes in opposite direction around the nucleus.

All d-orbital has four lobes ponting towards the corners of a square except dz2 . It has clover leaf shape. dz2 has two lobes only.

f-orbital has eight lobes pointing towards the corners of a cube.

Existance of orbitals: Quantum numbers of an orbital will tell us weather an orbital can exist or not.

1p: Principle quantum number (n) = 1; Azimuthal quantum number (l) = 1 (for p-orbital, l = 1)

This orbital will not exist because l cannot be equal to n. l has values ranging from 0 to (n-1)

2s: n = 2, l = 0 (for s-orbital), ml = 0. This orbital will exist.

2d: n = 2; l = 2. This orbital will not exist.

3p: n = 3, l = 1, ml = -l to +l, This orbital will exist.

3d: n = 3, l = 2. It will exist.

3f: n = 3, l = 3 (for f-orbital). It will not exist.

4g: n = 4, l = 4. It will not exist.

(C) Set of quantum numbers that will be acceptable.

(1, 0, 1/2, 1/2). This is not acceptable. It can be explaned as, l = 0, ml = -l to +l = 0

Hence ml = 0. But in the given set of quantum numbers ml = 1/2.

(2, 2, 1, 1/2). This is not acceptable. n = 2, l = 0 to (n-1) = 0 to (2-1) = 0 , 1. But l = 0 in the given set of quantum numbers.

(3, 0, 0, 1/2). It is acceptable. It designates 3s orbital.

(3, 2, 1, 1). It is not acceptable. spin quantum number ms can be either +1/2 or -1/2. But it is equal to 1 in the given set of quantum numbers.

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