Question

how many atoms of calcium are in the average human body? express your answer in scientific notation with two decimal places. show avogadros number
atoms of calcium show calculator show periodic...

Explanation:

Step1: Recall relevant data

The average human body contains about 1.0 kg of calcium (we can also use other sources, but a common value for mass of calcium in human body is around 1000 g, or we can use more precise: the mass of calcium in an average 70 - kg human is about 1.0 kg = 1000 g. The molar mass of calcium (Ca) is 40.08 g/mol (from periodic table). Avogadro's number $N_A = 6.022\times10^{23}$ atoms/mol.

Step2: Calculate moles of calcium

Moles of Ca, $n=\frac{\text{mass}}{\text{molar mass}}=\frac{1000\ g}{40.08\ g/mol}\approx24.95\ mol$

Step3: Calculate number of atoms

Number of atoms, $N = n\times N_A=24.95\ mol\times6.022\times10^{23}\ atoms/mol$

First, calculate $24.95\times6.022$: $24.95\times6.022 = 24.95\times6+24.95\times0.022=149.7 + 0.5489 = 150.2489$

Then, $N = 150.2489\times10^{23}=1.502489\times10^{25}\approx1.50\times10^{25}$ (with two decimal places in scientific notation)

Answer:

$1.50\times10^{25}$