Question

Calculate the total mass of the protons and electrons in 19/9F. Use 1.007825 amu as the mass of 1/1H(mass of a proton and an electron). Express your answer in atomic mass units to 6 significant figures. Calculate the total mass of the neutrons in 19/9F. Use 1.008665 amu as the mass of 1/0N(mass of a neutron). Express your answer in atomic mass units to 7 significant figures. Calculate the mass defect of 19/9F. Use 18.9984 amu as the actual mass of 19/9F. Express your answer in atomic mass units to the fourth decimal place.

Answer 1

Concepts and reason

The concept used to solve this problem is based on mass defect of an atom.

The mass defect of an atom is calculated with the help of actual mass of the atom and calculated mass. The mass of atom is equal to the sum of mass of electrons, protons and neutrons.

Fundamentals

The nuclear symbol of any atom is represented as follows:

$_Z^Y{\rm{A}}$

Here, A is atomic symbol of the element, Y is mass number of the element and Z is atomic number of the element.

The formula for mass defect is written as follows:

$d = {m_{\rm{c}}} - {m_{\rm{a}}}$

Here, ${m_{\rm{c}}}$ is calculated mass and ${m_{\rm{a}}}$ is actual mass of the atom.

(1)

First write the nuclear symbol as follows:

$_9^{19}{\rm{F}}$

Thus, atomic number of the atom is 9. Thus, the element contains 9 electrons $\left( E \right)$ and 9 protons $\left( P \right)$ .

The mass of electron and proton is equal to $_1^1{\rm{H}}$ = $1.007825{\rm{ amu}}$ .

Since, there are 9 electrons and 9 protons. Thus, total mass of electrons and proton is calculated by multiplying the sum of mass of electrons and protons with 9.

$\begin{array}{c}\\{\rm{Total mass of electron and proton}} = 9 \times {\rm{Mass of }}_1^1{\rm{H}}\left( {{\rm{mass of electron and proton}}} \right)\\\\ = 9 \times 1.007825{\rm{ amu}}\\\\ = 9.07043{\rm{ amu}}\\\end{array}$

(2)

First, calculate the number of neutrons as follows:

$\begin{array}{c}\\{\rm{Number of neutrons = Mass number}} - {\rm{atomic number (number of protons)}}\\\\ = 19 - 9\\\\ = 10\\\end{array}$

The mass of neutron is $1.008665{\rm{ amu}}$ .

Since, there are 10 neutrons. Thus, total mass of neutrons is calculated by multiplying the mass of neutrons with 10.

$\begin{array}{c}\\{\rm{Mass of nuetrons}} = 10 \times 1.008665{\rm{ amu}}\\\\ = 10.08665{\rm{ amu}}\\\end{array}$

(3)

Add mass of electrons/mass of protons and mass of neutrons for total mass of the atom as shown below:

$\begin{array}{c}\\{\rm{Calculated nuclear mass}} = {\rm{Mass of electron and proton + mass of nuetron}}\\\\{\rm{ = 9}}{\rm{.07043 amu}} + {\rm{10}}{\rm{.08665 amu}}\\\\{\rm{ = 19}}{\rm{.15708 amu}}\\\end{array}$

Now, mass defect is calculated as follows:

$\begin{array}{c}\\\Delta {\rm{m}} = {\rm{ Calculated total mass of }}_9^{19}{\rm{F}} - {\rm{actual total mass of }}_9^{19}{\rm{F}}\\\\ = {\rm{19}}{\rm{.15708 amu}} - {\rm{18}}{\rm{.9984 amu}}\\\\ = {\rm{0}}{\rm{.1587 amu}}\\\end{array}$

Ans: Part 1

Total mass of protons and electrons in $_9^{19}{\rm{F}}$ is $9.07043{\rm{ amu}}$ .

Part 2

Total mass of neutrons in $_9^{19}{\rm{F}}$ is ${\rm{10}}{\rm{.08665 amu}}$ .

Part 3

The mass defect in $_9^{19}{\rm{F}}$ is ${\rm{0}}{\rm{.1587 amu}}$ .