Understanding Atomic Mass
To find the mass of a single atom, we must bridge the gap between the macroscopic world (what we can weigh in a lab) and the microscopic world of individual atoms. In chemistry, we use the mole as a bridge.
The Fundamental Constants
To solve this, we need two key pieces of information:
- Molar Mass of Hydrogen ($M$): The atomic mass of hydrogen is approximately $1.008 \text{ g/mol}$. This means that one mole ($6.022 \times 10^{23}$ atoms) of hydrogen weighs $1.008 \text{ grams}$.
- Avogadro's Number ($N_A$): This is the number of particles in one mole, defined as $6.022 \times 10^{23} \text{ atoms/mol}$.
Step-by-Step Calculation
We can treat this as a simple unit conversion problem using the formula:
$$\text{Mass of one atom} = \frac{\text{Molar Mass}}{N_A}$$
Step 1: Set up the equation
Substitute the known values into the equation: $$\text{Mass} = \frac{1.008 \text{ g/mol}}{6.022 \times 10^{23} \text{ atoms/mol}}$$
Step 2: Perform the division
When you divide $1.008$ by $6.022$ and adjust for the scientific notation ($10^{23}$), you get:
$$\text{Mass} \approx 0.16738 \times 10^{-23} \text{ g}$$
Step 3: Express in standard scientific notation
To make it standard, we shift the decimal point one place to the right:
$$\text{Mass} \approx 1.67 imes 10^{-24} \text{ grams}$$
Conclusion
A single atom of hydrogen is incredibly light, weighing approximately $1.67 \times 10^{-24}$ grams. This tiny mass highlights the nature of atoms, which are the fundamental building blocks of matter, far too small to be weighed by standard laboratory scales.