Why is $N{{H}_{3}}$more basic than $P{{H}_{3}}$?

Hint: Basicity of elements decreases down the group as the size of the atom increases which further reduces the electron density. The size of the nitrogen atom is 155 pm while the size of the phosphorus atom is 195 pm.

Complete step by step solution:
-Nitrogen and phosphorus both elements belong to group 15.
-Nitrogen has atomic number 7 and is the lightest member of the group 15. Group 15 elements are also called pnictogens. At standard temperature and pressure, nitrogen is found to exist in a diatomic state which is a colourless and odourless gas with formula ${{N}_{2}}$.
-Phosphorus has the atomic number 15 and in elemental states exists in two forms, white phosphorus and red phosphorus. Because phosphorus is highly reactive, it is never found as a free element on earth.
-Nitrogen atom has seven electrons in the ground state and is arranged in the electronic configuration $1{{s}^{2}},2{{s}^{2}},2{{p}_{x}}^{1}2{{p}_{y}}^{1}2{{p}_{z}}^{1}$. Therefore the valency of nitrogen is +5 which is present in 2s and 2p orbitals. Nitrogen is one of the elements bearing the highest electronegativity as 3.04 on the Pauling scale which is exceeded only by chlorine (3.16), oxygen (3.44), and fluorine (3.98).
-Phosphorous is a multivalent nonmetal of the pnictogen family. Phosphorus has an atomic configuration as $1{{s}^{2}},2{{s}^{2}}2{{p}^{6}},3{{s}^{2}},3{{p}_{x}}^{1}3{{p}_{y}}^{1}3{{p}_{z}}^{1}$ with five valence electrons found in the s and p orbitals of the highest energy level of the electron configuration. Phosphorus has an electronegativity of 2.19 on the Pauling scale.
-Nitrogen being the smallest member of its group can easily donate its lone pair of electrons, on the other side, phosphorus being bigger than nitrogen, therefore, will not readily donate its lone pair of electrons. The species which will more readily donate an electron pair will be more basic. Hence $N{{H}_{3}}$ is more basic than $P{{H}_{3}}$.
-Also, the P-H bonds $P{{H}_{3}}$ are weaker than the N-H bonds $N{{H}_{3}}$. This is because, nitrogen being more electronegative, pulls the electrons bond towards itself creating more polar bond than the P-H bond.
These were the reasons why $N{{H}_{3}}$ is more basic than $P{{H}_{3}}$.

Note: Let us now see the importance of nitrogen and phosphorous compounds.
-Nitrogen is the most common pure element in the earth, constituting around 78.1% of the entire volume of the atmosphere. Compounds of nitrogens constantly interchange between the atmosphere and living organisms. The usable form of nitrogen is usually ammonia which is used first by plants. Nitrogen compounds are found in the DNA and RNA of the human body in the form of nitrogenous bases.
-Phosphorus is an essential element of life. Compounds of phosphorus are found abundantly in living organisms in various forms, like phosphates which is a component of DNA, RNA, ATP, and phospholipids. First elemental phosphorus was discovered from human urine and bone ash which was at that time considered the only source of phosphorus.