Answer:
Explanation:
Data given:
Values for four Quantum number for
1. 4f⁶ = ?
2. 3s¹ = ?
3. last electron to fill ²⁸Ni = ?
4. for the outermost electron in ²²Ti = ?
Solution:
Atom is made up of electron, proton and neutron. electron revolve in the orbital around the nucleus and can be identified by its quantum number.
the quantum number of an electron give information about the energy and position of the electron in atom
General formulas to calculate quantum number
There are 4 quantum numbers that have its own specification
1. Principal quantum number:
it give us information about main shells
it is represented by "n" and can be 1, 2, 3, 4 ,5 ......so on
So,
Principal quantum number = n
2. Azimuthal quantum number
it give us information about angular momentum and shape of orbitals
it is denoted by "l" and can be 0, 1, 2, 3, 4 ,5 ......so on
So,
Azimuthal quantum number = l and calculated by n-1 formula
3. Magnetic quantum number
it give us information about orbitals available in a sub-shell and orientation of orbitals in space
it is denoted by "m" and can be (-l, 0, +l) i.e -1, 0, +1
Magnetic quantum number = m and calculated by -l, 0, +1 formula
4. Spin quantum number
it give us information about spin of electron around its axis in orbital
it is denoted by "s"
it can be +1/2 or -1/2
Spin quantum number = +1/2 or -1/2
now calculate for each one by one
_____________________
1. 4f⁶
- Principal quantum number = n= 4
- Azimuthal quantum number = l = n-1
put values in formula
n-1 = 4-1 = 3
Azimuthal quantum number = l = 3
- Magnetic quantum number = m
calculated by -l, 0, +l formula
So, l = 3 so "m" will be
-3, -2, -1, 0, +1, +2, +3
- Spin quantum number = +1/2 or -1/2
_____________________
2. 3s¹ =
- Principal quantum number = n= 3
- Azimuthal quantum number = l = n-1
put values in formula
n-1 = 3-1 = 2
Azimuthal quantum number = l = 3
- Magnetic quantum number = m
calculated by -l, 0, +l formula
So, l = 2 so m will be
-2, -1, 0, +1, +2,
- Spin quantum number = +1/2 or -1/2
___________________________
3. last electron to fill ²⁸Ni = ?
first we will look for the electronic configuration of ²⁸Ni
configuration of ²⁸Ni = [Ar], 3d⁸, 4s²
So the last electrons to fill is 4s²
- Principal quantum number = n= 4
- Azimuthal quantum number = l = n-1
put values in formula
n-1 = 4-1 = 3
Azimuthal quantum number = l = 3
- Magnetic quantum number = m
calculated by -l, 0, +l formula
So, l = 2 so m will be
+3, -2, -1, 0, +1, +2, +3
- Spin quantum number = +1/2 and -1/2
____________________
4. for the outermost electron in ²²Ti = ?
first we will look for the electronic configuration of ²²Ti
configuration of ²²Ti = [Ar], 3d²
So the last electrons to fill is 3d²
- Principal quantum number = n= 3
- Azimuthal quantum number = l = n-1
put values in formula
n-1 = 3-1 = 2
Azimuthal quantum number = l = 2
- Magnetic quantum number = m
calculated by -l, 0, +l formula
So, l = 2 so m will be
-2, -1, 0, +1, +2
- Spin quantum number = +1/2 or -1/2
