Question

Calculate the mass defect for the formation of phosphorus-31. The mass of a phosphorus-31 nucleus is 30.973765 amu. The masses of a proton and a neutron are 1.00728 and 1.00866 amu, respectively. Enter your answer in amu's with five decimal places and no units.

Answer 1

Answer: The mass defect for the formation of phosphorus-31 is 0.27399

Step-by-step explanation:

Mass defect is defined as the difference in the mass of an isotope and its mass number.

The equation used to calculate mass defect follows:

`\Delta m=[(n_p* m_p)+(n_n* m_n)]-M`

where,

`n_p` = number of protons

`m_p` = mass of one proton

`n_n` = number of neutrons

`m_n` = mass of one neutron

M = mass number of element

We are given:

An isotope of phosphorus which is
`_(15)^(31)\textrm{P}`

Number of protons = atomic number = 15

Number of neutrons = Mass number - atomic number = 31 - 15 = 16

Mass of proton = 1.00728 amu

Mass of neutron = 1.00866 amu

Mass number of phosphorus = 30.973765 amu

Putting values in above equation, we get:

`\Delta m=[(15* 1.00728)+(16* 1.00866)]-30.973765\\\\\Delta m=0.27399`

Hence, the mass defect for the formation of phosphorus-31 is 0.27399