32 PE - College Physics (Urone)

Question

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

Step-by-Step Solution

Answer

The number of atoms in the bacterium are 10¹¹.

Atoms in bacterium

The number of atoms in a bacterium is 

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

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

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

Deriving conclusions

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