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Answer: (a) seven orbitals, (b). 3 orbitals, (c). 5 orbitals and (d). 4 orbitals.

Explanation:

In order to solve this question we need to know how to explain the behaviour of electrons in atoms,and what we need to know is what is called the quantum numbers. There are four different kinds of quantum numbers and they are;

(1). Principal quantum numbers: the principal quantum number is denoted by the letter 'n'. It is used to describe the orbitals' energy. It has the values of n=1,2,3,4,...

(2). The spin quantum numbers: the spin quantum numbers is denoted by m(s). The 's' in the parenthesis is in subscript. It has the values of +1/2 and -1/2.

(3). Azimuthal quantum numbers: this is denoted by ℓ and it is used to explain orbital angular momentum and orbital shape. It has the values of ℓ= 0,1,2,3,....n-1.

Note that => ℓ = 0; we have a s-subshell,sphere shape.

ℓ = 1; p-subshell, dumb bell shape.

ℓ=2; d- subshell, double dumb bell shape.

ℓ= 3; f - subshell, multiple lobes.

(4). Magnetic quantum number: it is denoted by m(l) where the 'l' in the parenthesis is in subscript.

===> NOTE: there are (2ℓ + 1 ) orbitals in a subshell, also, there are n^2 number of orbitals in a shell.

Having known all that above, let us jump right in to the solution.

(a). From above we can see that; there are (2ℓ + 1 ) orbitals' in a subshell, also, f= ℓ= 3.

Therefore, the number of orbitals in 5f = 2 ℓ + 1 = (2×3) + 1 = 6+1 = 7 orbitals for 5f.

(b). 4p, the numbers of orbitals in 4p is; p= ℓ= 1=> 4 ℓ + 1 = (2×1) + 1 = 2+1 = 3 orbitals for 4p.

(c). 5d, the numbers of orbitals' in 5d is; d= ℓ= 2 = (2×2) + 1 = 4 + 1 = 5 orbitals for 5d.

(d). For n= 2, the numbers of orbital is ; n^2. Where the n given is 2. Therefore, 2^2= 2×2 = 4 orbitals in n=2.

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An orbital refers to a region in space where electrons can be found.

An orbital refers to a region in space where there is a high probability of finding an electron. Orbitals that posses the same amount of energy are called degenerate orbitals.

The number of orbitals in an atom that can have the following designations are shown below;

  • 5f - seven orbitals can have this designation because the f orbital is seven fold degenerate.
  • 4p - three orbitals can have this designation because the p orbital is three fold degenerate
  • 5d - five orbitals can have this designation because the d orbital is five fold degenerate
  • n = 2 - the total number of orbitals in an energy level is given by n^2. Hence there are four orbitals that has the designation n =2

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