Answer:

Introduction:
The four quantum numbers (n, l, m, s) are used to describe the properties of electrons in an atom. Each electron in an atom has a unique set of quantum numbers that determines its energy level, shape of its orbital, orientation in space, and its spin.

Given Information:
The given values of the four quantum numbers are:
n = 4
l = 0
m = 0
s = 1/2

Explanation:
To determine the element based on the given quantum numbers, we need to understand the significance of each quantum number and its relation to the electronic configuration of an atom.

1. Principal Quantum Number (n):
The principal quantum number (n) represents the energy level or shell in which the electron is present. It can have whole number values starting from 1. In this case, the value of n is 4, indicating that the electron is in the fourth energy level.

2. Azimuthal Quantum Number (l):
The azimuthal quantum number (l) represents the shape of the orbital or subshell. It can have values ranging from 0 to (n-1). In this case, the value of l is 0, indicating that the electron is in an s orbital.

3. Magnetic Quantum Number (m):
The magnetic quantum number (m) represents the orientation of the orbital in space. It can have values ranging from -l to +l. In this case, the value of m is 0, indicating that the electron is in an s orbital with no specific orientation.

4. Spin Quantum Number (s):
The spin quantum number (s) represents the spin of the electron. It can have two values, +1/2 (spin-up) or -1/2 (spin-down). In this case, the value of s is 1/2, indicating that the electron has a spin-up orientation.

Determining the Element:
Based on the given quantum numbers (n=4, l=0, m=0, s=1/2), we can conclude that the valence electron is in the 4s orbital. The electron configuration of the element can be represented as [Ar] 4s^1, where [Ar] represents the noble gas configuration of the previous energy level.

The only element among the given options that has a valence electron configuration of [Ar] 4s^1 is Potassium (K). Therefore, the correct answer is option b) K.

Conclusion:
The element with the given quantum numbers (n=4, l=0, m=0, s=1/2) is Potassium (K).

Electronic configuration of k (at no. 39)is 2/8/18/1. In this no. Of shell is 4. n=4.and last valence electron is in s subshell. For s subshell the value of l=0.for l=0,m also=0.and value of spin quantum no. (s) is +1/2bacause only 1 electron is present having upward spin which is +1/2.hence correct answer is b) k