How many atoms are there in the earth?

Question

Earth has a mass of 5.98 x 10^24 kg. Average mass of the atoms that make up earth is 40u. The answer is 9.0 x 10^49. Could you show me the steps involved in solving this?

Answer 1

not enough room on here for a number that large!

Answer 2

To find the number of atoms, just divide the mass of earth with mass of an atom.

Answer 3

6

Answer 4

First convert atomic mass unit into kilograms:

40 u x (1.66 x 10^-27 kg) = 6.64 x 10^-26 kg

Now use the ratio of the mass of Earth and the average atomic mass on Earth to find the number of atoms:

(5.98 x 10^24 kg) / (6.64 x 10^-26 kg) = 9.01 x 10^49

Answer 5

The chemical composition of the Earth (by mass) is:

34.6% Iron

29.5% Oxygen

15.2% Silicon

12.7% Magnesium

2.4% Nickel

1.9% Sulfur

The mass of the Earth is 5.97e24 kg = 5.97e27 g

Therefore the earth contains

2.07e27g Iron

1.76e27g Oxygen

9.1e26g Silicon

7.6e26g Magnesium

1.4e26g Nickel

1.1e26g Sulfur

The molar masses of these elements are:

55.9g Iron

16.0g Oxygen

28.1g Silicon

24.3g Magnesium

58.7g Nickel

32.1g Sulfur

Therefore the number of moles of each of these elements is:

3.7e25 Iron

1.10e26 Oxygen

3.2e25 Silicon

3.1e25 Magnesium

2e24 Nickel

3e24 Sulfur

for a total of 2.15e26 moles. Multiply by Avogadro's number to get number of atoms = 1.3e50 or so.

(what about the earth's atmoshere?)

Answer 6

1u = 1/6.022*10^23 =1..661*10^-24g

40 u= 40*1.661*10^-24=6.64*10^-23g= 6.64*10^-26kg

and you divide mass of earth by this numbe

5.98*10^24/6.64*10^-26=9*10^-49

Answer 7

All you need to know is the relation between "u" (units of atomic mass) and Kg which is this:

1 u = 1’66 x 10^27 kg

We consider that all mass in Earth are atoms, so just divide the total mass of the Earth by the mass of a bearing in mind that one atom weighs (averagely) 40x1’66 · 10(-27) kg

So, Answer:

5.98 x 10^24 kg / [40 x 1,66 x 10^-27] = 0,09006 x 10^51

Which can also be written as: 9 x 10^49 atoms in the Earth, just right what you wanted :)