# Question 138bc

Dec 1, 2017

Number of Protons: \qquad N_p = Z.N = 52.50\times10^{20};
Number of Electrons: \qquad N_e = Z.N = 52.50\times10^{20};
Number of Neutrons: $\setminus q \quad {N}_{n} = \left(A - Z\right) . N = 56.00 \setminus \times {10}^{20}$

#### Explanation:

Though Phosphorous has 23 isotopes, only one of it is stable. The only stable isotope of phosphorous is Phosphorous-31. Almost all of the naturally occurring phosphorous is in this form.

Phosphorous-31 has an atomic number of $Z = 15$ and mass number of $A = 31$. That means, each phosphorous-31 atom has 15 protons, 15 electrons and $A - Z = 16$, neutrons.

To calculate the total number of electrons, protons and neutrons in a certain mass of phosphorous, first find the total number of phosphorous-31 atoms.

The number of phosporous atoms in $m$ grams of phosphorous is:

$N = {N}_{A} . \left(\frac{m}{M} _ p\right)$, where ${N}_{A}$ is the Avogadro Number and ${M}_{p}$ is the molar mass of phosphorous in grams/mole.

N_A = 6.023\times10^{23}\quad mol^{-1}; \qquad M_p = 30.97376\quad g/(mol);
m = 0.018 g;

$N = 3.500 \setminus \times {10}^{20}$

Number of Protons: \qquad N_p = Z.N = 52.50\times10^{20};
Number of Electrons: \qquad N_e = Z.N = 52.50\times10^{20};#
Number of Neutrons: $\setminus q \quad {N}_{n} = \left(A - Z\right) . N = 56.00 \setminus \times {10}^{20}$