Q57P - University Physics with Modern Physics

Question

Estimate the number of atoms in your body. (Hint: Based on what you know about biology and chemistry, what are the most common types of atom in your body? What is the mass of each type of atom? Appendix $D$ gives the atomic masses of different elements, measured in atomic mass units; you can find the value of an atomic mass unit, or 1 in Appendix E.)

Step-by-Step Solution

Answer

Water is the most common type of atom found in the human and the mass of water is $2.99\times {10}^{-26} \mathrm{kg}$ and the total number of atoms is $7.02\times {10}^{27}$ atom.

Step 1: Identification of given data

The given data from Appendix D can be listed below,

• The atomic mass of water is, $A=18.015\mathrm{U}$
• The value of amu is, $1\mathrm{amu}=1.661\times {10}^{-27} \mathrm{kg}/\mathrm{ul}$

Step 2: Concept/Significance of atomic mass

Protons and neutrons have almost similar masses, the number of protons plus neutrons in an atom corresponds to the number of atomic mass units (amu).

Step 3: Determination of the most common type of atom in the human body and its mass

Water is the most common type of atom found in the human body.

Mass of water atom is given by,

$\begin{array}{rcl}m& =& (18.015\mathrm{u})\left(1.661\times {10}^{-27} \mathrm{kg}/\mathrm{u}\right)\\ & =& 2.99\times {10}^{-28} \mathrm{kg}\end{array}$

Thus, mass of the most common type of atom is $2.99\times {10}^{-26} \mathrm{kg}$.

Let's say a person has $70 \mathrm{kg}$ weight. So, the number of molecules is,

$\begin{array}{rcl}M& =& \frac{70 \mathrm{kg}}{m}\\ & =& \frac{70 \mathrm{kg}}{2.99\times {10}^{-28} \mathrm{kg}/\text{ molecule }}\\ & =& 2.34\times {10}^{27}\mathrm{molecules}\end{array}$

Water molecules contain 3 atoms, so the total number of atoms is,

$\begin{array}{rcl}\mathrm{n}& =& 3\times \left(2.34\times {10}^{27}\right)\\ & =& 7.02\times {10}^{27}\text{ atoms }\end{array}$

Thus, the mass of water is $2.99\times {10}^{-26} \mathrm{kg}$ and the total number of atoms is $7.02\times {10}^{27}$ atoms .