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Chapter 1: 32 PE (page 11)

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 10-27kg and the mass of a bacterium is on the order of 10-15kg.)

Short Answer

Expert verified

The number of atoms in the bacterium are 1011.

Step by step solution

01

Atoms in bacterium

The number of atoms in a bacterium is

\({\rm{Number of atoms = }}\frac{{{\rm{Mass\;of\;bacterium}}}}{{{\rm{10 \times average\;mass\;of\;a\;hydrogen\;atom}}}}\)

02

Solving for given mass

Rewrite the equation for number of atoms as below.

\({\rm{Number of atoms = }}\frac{{{\rm{Mass\;of\;bacterium}}}}{{{\rm{10 \times average\;mass\;of\;a\;hydrogen\;atom}}}}\)

Substitute 10-27kg for average mass of an atom and 10-15 kg for mass of bacterium.

\(\begin{array}{c}Number{\rm{ }}of{\rm{ atoms}} = \frac{{{{10}^{ - 15}}{\rm{ }}kg}}{{10 \times {{10}^{ - 27}}{\rm{ }}kg}}\\ = {10^{11}}\end{array}\)

03

Deriving conclusions

Hence, the number of atoms in the bacterium are 1011.

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