32. Calculate the approximate number of atoms in a...

32. Calculate the approximate number of atoms in a bacterium. Assume that the average mass of an atom in the bacterium is ten times the mass of a hydrogen atom. (Hint: The mass of a hydrogen atom is on the order of $10^{-27} \mathrm{kg}$ and the mass of a bacterium is on the order of $10^{-15} \mathrm{kg.}$ .

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Key Concepts

Order of Magnitude Estimation

This concept involves using rough estimates of powers of ten to simplify calculations for quantities that span many orders of magnitude. It allows one to evaluate the scale of numbers without needing exact figures, which is especially useful in fields like astrophysics or microbiology where quantities can vary widely.

Scientific Notation

Scientific notation is a way to express very large or very small numbers as a product of a number and a power of ten. This is essential in performing calculations with orders of magnitude and helps maintain clarity and manageability of numbers in physics and engineering.

Division-Based Calculation

This technique involves calculating the number of constituent units (such as atoms) by dividing the total mass of an object by the mass of an individual unit. It is a fundamental method in physics for determining quantities from aggregate metrics when the mass per unit is known.

Atomic Mass and Estimation Assumptions

This concept emphasizes the use of an average atomic mass to represent the typical mass of atoms in a system. In estimation problems, it is common to base calculations on standard values (like the mass of a hydrogen atom) with adjustments made for the specific context, allowing for simplified, yet realistic, modeling of the problem at hand.

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