Question

Use table 1-3 to estimate the total number of protons or neutrons in (a) a bacterium, (b) a DNA molecule, (c) the human body, and (d) the galaxy.

Short answer

The number of protons or neutrons in (a) a bacterium is \({10^{12}}\), in (b) a DNA molecule is \({10^{10}}\), in (c) the human body is \({10^{29}}\), and in (d) the galaxy is \({10^{68}}\).

Step-by-step solution

Step 1:  Meanings of proton and neutron

A neutron may be defined as a subatomic particle, and it is considered one of the building blocks of the atom.

A proton may be defined as an electrically charged particle, and the charge on the proton is positive. It is positioned within the nucleus of the atom.

Data from table 1-3

From table 1-3:

The mass of the bacterium is \({M_B} = {10^{ - 15}}\;{\rm{kg}}\).

The mass of the DNA molecule is \({M_D} = {10^{ - 17}}\;{\rm{kg}}\).

The mass of the human body is \({M_H} = {10^2}\;{\rm{kg}}\).

The mass of the galaxy is \({M_G} = {10^{41}}\;{\rm{kg}}\).

The mass of the proton or neutron is \({m_{P,N}} = {10^{ - 27}}\;{\rm{kg}}\).

Calculate the number of protons or neutrons in a bacterium

The number of protons or neutrons in a bacterium can be calculated as

\(\begin{aligned}{l}{N_B} = \frac{{{M_B}}}{{{m_{P,N}}}}\\{N_B} = \frac{{\left( {{{10}^{ - 15}}\;{\rm{kg}}} \right)}}{{\left( {{{10}^{ - 27}}\;{\rm{kg}}} \right)}}\\{N_B} = {10^{12}}\end{aligned}\).

Thus, the number of protons or neutrons in a bacterium is \({10^{12}}\).

Calculate the number of protons or neutrons in a DNA molecule

The number of protons or neutrons in a DNA molecule can be calculated as

\(\begin{aligned}{l}{N_D} = \frac{{{M_D}}}{{{m_{P,N}}}}\\{N_D} = \frac{{\left( {{{10}^{ - 17}}\;{\rm{kg}}} \right)}}{{\left( {{{10}^{ - 27}}\;{\rm{kg}}} \right)}}\\{N_D} = {10^{10}}\end{aligned}\).

Thus, the number of protons or neutrons in a DNA molecule is \({10^{10}}\).

Calculate the number of protons or neutrons in the human body

The number of protons or neutrons in the human body can be calculated as

\(\begin{aligned}{l}{N_H} = \frac{{{M_H}}}{{{m_{P,N}}}}\\{N_H} = \frac{{\left( {{{10}^2}\;{\rm{kg}}} \right)}}{{\left( {{{10}^{ - 27}}\;{\rm{kg}}} \right)}}\\{N_H} = {10^{29}}\end{aligned}\).

Thus, the number of protons or neutrons in the human body is \({10^{29}}\).

Calculate the number of protons or neutrons in the galaxy

The number of protons or neutrons in the galaxy can be calculated as

\(\begin{aligned}{l}{N_G} = \frac{{{M_G}}}{{{m_{P,N}}}}\\{N_G} = \frac{{\left( {{{10}^{41}}\;{\rm{kg}}} \right)}}{{\left( {{{10}^{ - 27}}\;{\rm{kg}}} \right)}}\\{N_G} = {10^{68}}\end{aligned}\).

Thus, the number of protons or neutrons in the galaxy is \({10^{68}}\).