Give the orbital designations of electrons with the following quantum numbers"
(a) n = 3, l = 0, m1=0
(b) n=2, l=1, ml=-1
(c) n=4, l=3, ml=-2
(d) n=4, l=2, ml=0
To determine the orbital designation of electrons with the given quantum numbers, we need to understand the different quantum numbers and their relationship to the electron orbitals.
The four quantum numbers that describe an electron are:
1. Principal Quantum Number (n): Represents the energy level or the distance from the nucleus. It takes integer values from 1 onwards.
2. Azimuthal Quantum Number (l): Determines the shape of the orbital and can have values ranging from 0 to (n-1).
3. Magnetic Quantum Number (ml): Specifies the orientation of the orbital in space and can have values ranging from -l to +l.
4. Spin Quantum Number (ms): Describes the spin of the electron, which can either be +1/2 (up) or -1/2 (down).
Now let's determine the orbital designations of electrons with the given quantum numbers.
(a) n = 3, l = 0, ml = 0:
For the given quantum numbers, l = 0, which means it is an s orbital. The s orbital has only one possible orientation, ml = 0. Therefore, the orbital designation is 3s.
(b) n = 2, l = 1, ml = -1:
Here, l = 1, which corresponds to the p orbital. Since l = 1, there are three possible orientations: ml = -1, 0, +1. Therefore, the orbital designation is 2p.
(c) n = 4, l = 3, ml = -2:
When l = 3, the orbital type is d. For l = 3, there are seven possible orientations: ml = -3, -2, -1, 0, +1, +2, +3. In this case, ml = -2. Therefore, the orbital designation is 4d.
(d) n = 4, l = 2, ml = 0:
For l = 2, the orbital type is f. With l = 2, there are five possible orientations: ml = -2, -1, 0, +1, +2. Here, ml = 0, so the orbital designation is 4f.
Therefore, the orbital designations of electrons with the given quantum numbers are:
(a) 3s
(b) 2p
(c) 4d
(d) 4f