Question #138bc

1 Answer
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: \qquad N_n = (A-Z).N = 56.00\times10^{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.(m/M_p), 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\times10^{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: \qquad N_n = (A-Z).N = 56.00\times10^{20}