Question

Question #138bc

Answer 1

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}`