Question

The human body contains about 10^(14) cells, and the diameter of a typical cell is about 10 micrometers. Like all ordinary matter, cells are made of atoms; a typical atomic diameter is 0.1 nanometers. I have all of the correct answers, but I do not know how to get to these answers or solve them on my own. I would like to get explanations (why?) and see how it should be done (math being done). a) How does the number of atoms in a cell compare with the number of cells in the body? The answer is "should be the same". b) The volume of the cell is about The answer is 10^(-15) m^3. c) The mass of the cell is about The answer is 10^(-12) kg. d) The number of atoms in the body is closest to The answer is 10^(30). Thanks.

Answer 1

a) Here, Diameter of atom = 0.1 x 10^-9 meter (1 nanometer = 10^-9 meter)

Vol of sphere = (pi x D³ )/6 Where, D is Diameter of sphere

Therefore, Volume of one atom = (3.14 x (0.1 x 10^-9)³) / 6

= 5.23 x 10^-31 m³/atom

Same, Volume of one Cell = (3.14 x (10 x 10^-6)³)/6 (1 micrometer = 10^-6 meter)

= 5.23 x 10^-16 m3/cell

Now, Cell are made of atoms

So, No of Atomes in a cell = (5.23 x 10^-16)/(5.23 x 10^-31) (m3/cell)/(m3/atom)

= 10¹⁵ atom / cell

Which is equal to 10¹⁴= 1 x 10¹⁵ cell / Body

Therefore No of atoms in a cell should be the same as no of cells in a body

b ) Volume of one Cell = (3.14 x (10 x 10^-6)³)/6

= 0.523 x 10^-15 m3/cell (1 micrometer = 10^-6 meter)

c ) mass of one atom = 1.67 x 10^-24 grams / atom

= 1.67 x 10^-27 kilograms / atom

mass of cell = mass of atom x (no of atom / cell)

= (1.67 x 10^-27) x (10¹⁵)

= 1.67 x 10^-12 kg / cell

d ) No of atoms in a body = (No of cell in a body) x (No of atoms in a cell)

= (1 x 10¹⁵ ) x (10¹⁵)

= 10³⁰ atoms / Body