Question

Please help, I don't understand, 25 points
What does a set of four quantum numbers tell you about an electron? Compare and contrast the locations and properties of two electrons with quantum number sets (4, 3, 1, +½) and (4, 3, -1, +½).

Answer 1

The four quantum numbers are n, l, m and s

'n' is the Principle Quantum Number which is also known as the energy level (the total number of shells of an atom)

'l' is the Azimuthal Quantum Number which is the angular momentum of the electron

'm' is the Magnetic Quantum Number which tells the magnetic moment of the electron

's' is the Spin Quantum Number which tells about the spin of an electron

All these numbers are used to find the locatin of an electron (just like a house address)

n is the shell number of the electron like in which shell is the electron located
l gives the angular momentum. Remember, l is always one less than n (i.e. n-1) For example, if n(number of shells) are 3 then l will be 2. If n is 4 then l will be 3
m is the magnetic moment (m ranges from -l to +l). If maximum value of l (angular momentum) is 3 then m will vary from -3 to +3 (will be written as -3, -2, -1, 0, 1, 2, 3)
s tells the direction of the spin of an electron. s can be +1/2 or -1/2 but we usually write +/-$\frac{1}{2}$. If spin is shown as ↑ then the value will be +1/2 and if it is shown as ↓ the value will be -1/2.

Let's do the questions:
1. The quantum set is (4, 3, 1, +1/2)
That means n = 4, l = 3, m = 1 and s = +1/2

2. Set is (4, 3, -1, +1/2)
Therefore n = 4, l = 3, m = -1, s = +1/2

If a question is given that: Find all the quantum numbers of an electron in the 4th shell.

Attemptation: n = 4, l = 3, m = -3, -2, -1, 0, 1, 2, 3 and s = +1/2, -1/2