Question

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. einstein’s equation e = mc² 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 × 10⁻⁴ amu, to show that the mass of a ¹²c atom is less than the sum of the masses of the constituent particles.

Explanation:

Step1: Determine the number of protons, neutrons and electrons in \(^{12}C\)

A \(^{12}C\) atom has 6 protons, 6 neutrons and 6 electrons.

Step2: Calculate the sum of the masses of the constituent particles

The mass of 6 protons is \(6\times1.0073\ \text{amu}=6.0438\ \text{amu}\).
The mass of 6 neutrons is \(6\times1.0087\ \text{amu} = 6.0522\ \text{amu}\).
The mass of 6 electrons is \(6\times5.486\times 10^{-4}\ \text{amu}=0.0032916\ \text{amu}\).
The sum of the masses of the constituent - particles \(m_{sum}=6.0438 + 6.0522+0.0032916\ \text{amu}=12.0992916\ \text{amu}\).

Step3: Find the actual mass of \(^{12}C\)

By definition, the mass of a \(^{12}C\) atom is exactly 12 amu.

Step4: Compare the two masses

Since \(12\ \text{amu}<12.0992916\ \text{amu}\), the mass of a \(^{12}C\) atom is less than the sum of the masses of the constituent particles.

Answer:

The mass of a \(^{12}C\) atom (12 amu) is less than the sum of the masses of 6 protons, 6 neutrons and 6 electrons (12.0992916 amu), which shows that the mass of a \(^{12}C\) atom is less than the sum of the masses of its constituent particles.