Boltzmann constant (k) is given by:
A. $k=R\times {{N}_{A}}$
B. $k=1.3807\times {{10}^{-21}}J{{K}^{-1}}$
C. $k=\dfrac{{{N}_{A}}}{R}$
D. $k=\dfrac{R}{{{N}_{A}}}$

Hint: Boltzmann constant is a physical constant that is denoted by (k or ${{k}_{B}}$). It gives a relation between the average kinetic energy of a particle and temperature of the gas.

Complete answer:
- Boltzmann constant is obtained by dividing gas constant (R) and Avogadro constant ${{N}_{A}}$.
- The relation between Boltzmann constant and the gas constant is given by: $k=\dfrac{R}{{{N}_{A}}}$
- Boltzmann constant also occurs in Boltzman’s entropy formula and Planck’s law of black-body radiation.
- The unit of Boltzmann constant is J/K. It is found that the value of Boltzman constant
is ${{k}_{B}}=1.3806452\times {{10}^{-23}}J/K$

Hence, we can conclude that the correct option is (D) that is Boltzmann constant (k) is given by $k=\dfrac{R}{{{N}_{A}}}$

Additional information:
- There are various applications of Boltzmann constant, it is used in diverse disciplines of chemistry. Some of them are:
- It is used to express the equipartition of energy of an atom.
- It is also useful and plays an important role in statistical definition of entropy.
-It is also used to express thermal voltage in semiconductors.
- It is also found that the kinetic energy for one mole of an ideal gas is given by the formula (3/2)RT and that is equal to (3/2)NkT.

Note:
- The Boltzmann constant helps us to relate the temperature of the molecule to its energy.
- The Boltzmann constant has the dimension of energy divided by temperature, which is the same as that of entropy. It has dimensional formula of $\left[ {{M}^{1}}{{L}^{2}}{{T}^{-2}}{{K}^{-1}} \right]$