Question

The maximum number of 4f electrons that can have $s = - \dfrac{1}{2}$ values is:
A. 14
B. 7
C. 5
D. 10

Answer 1

Hint: Quantum numbers are defined as the set of four quantities that define the complete behaviour of an electron within an atom. These four quantum numbers are described by the Schrodinger equation.

Complete step by step answer:
As per the question, the electrons are in the 4f shell, so as per the concept of quantum numbers, the principal quantum number (n) is 4. As we know the value of the secondary quantum number i.e. angular quantum number (l) is 0 to n-1. Thus for the above case, the value of l will be 0,1,2,3.
As we know for s orbital value of l is 0, for p orbital the value of l is 1, for d-orbitals the value of l is 2 and for f orbitals, the value of l is 3. As we know the electrons are in f orbitals then the value of the angular quantum number (l) is 3. As we know magnetic quantum numbers determine the number of orbitals. The magnetic quantum number as $ - l{\text{ to }}l$, where l is the angular quantum number. As from above, we found that the value of l =3 thus the value of m = -3 to 3 i.e. -3,-2,-1,0,1,2,3. Hence there are 7 orbitals and we know that each orbital contains a maximum two-electron of opposite spin thus a total number of the electrons in 4f orbitals is 14 having two opposite spin which can be given by spin quantum number(s). The value of the spin quantum number is ½ and -½. Thus the maximum number of an electron having spin quantum number -½ is exactly half of the total number of electron i.e. 7

So, the correct answer is Option B .

Note: The set of four quantum numbers is unique for each electron and these are important as the electron configuration can be determined using quantum numbers and also their approximate location in the atom. Also, the characteristics such as atomic radius and ionization energy of an atom can be determined using the same.