Question

1. describe what the isotopes of an element have in common and how they are different.
2. what makes an atom? provide an answer in complete sentences that describes the components of an atom and how those components relate to the atomic symbol for the various isotopes of an atom.

problems

1. estimate the mass of one $^{14}c$ atom (in amu) as precisely as you can (from the data in the model). explain your reasoning.
2. use the data in model 1 to estimate the values (in amu) of:

a) the mass of an electron
b) the mass of a proton
c) the mass of a neutron

1. the mass values calculated in problem 2 are only approximate because when atoms (up through iron) are made (mainly in stars) from protons, neutrons, and electrons, energy is released. einsteins equation $e = mc^2$ enables us to relate the energy released to the mass loss in the formation of atoms. use the known values for the mass of a proton, 1.0073 amu, the mass of a neutron, 1.0087, and the mass of an electron, $5.486\times10^{-4}$ amu, to show that the mass of a $^{12}c$ atom is less than the sum of the masses of the constituent particles.

Explanation:

Step 1: Recall atomic - mass unit concept

The atomic mass unit (amu) is defined such that the mass of a carbon - 12 ($^{12}$C) atom is exactly 12 amu. A $^{14}$C atom has 2 more neutrons than a $^{12}$C atom. The mass of a neutron is approximately 1 amu. So the mass of a $^{14}$C atom is approximately 14 amu.

Step 2: Mass of sub - atomic particles

a) The mass of an electron is extremely small compared to protons and neutrons. From standard data, the mass of an electron is approximately $5.486\times 10^{-4}$ amu.
b) The mass of a proton is approximately 1.0073 amu.
c) The mass of a neutron is approximately 1.0087 amu.

Step 3: Calculate mass of $^{12}$C and its constituent particles

A $^{12}$C atom has 6 protons, 6 neutrons, and 6 electrons.
The sum of the masses of its constituent particles is $m_{sum}=6\times(1.0073 + 1.0087)+6\times5.486\times 10^{-4}$
\[

$$\begin{align*} m_{sum}&=6\times(2.016)+6\times5.486\times 10^{-4}\\ &=12.096+ 0.0032916\\ &=12.0992916\text{ amu} \end{align*}$$

\]
The actual mass of a $^{12}$C atom is defined as 12 amu. So, $12\text{ amu}<12.0992916\text{ amu}$, which shows that the mass of a $^{12}$C atom is less than the sum of the masses of its constituent particles.

Answer:

1. The mass of one $^{14}$C atom is approximately 14 amu because it has 2 more neutrons than $^{12}$C and the mass of a neutron is approximately 1 amu.
2. a) The mass of an electron is approximately $5.486\times 10^{-4}$ amu.

b) The mass of a proton is approximately 1.0073 amu.
c) The mass of a neutron is approximately 1.0087 amu.

1. As calculated above, the sum of the masses of 6 protons, 6 neutrons, and 6 electrons is 12.0992916 amu, while the mass of a $^{12}$C atom is defined as 12 amu. So the mass of a $^{12}$C atom is less than the sum of the masses of its constituent particles.