Converting units question?

Question

The earth has a mass of 5.98X10^kg. The average mass of the atoms that make up the Earth is 40u. How many atoms are in the Earth??

(u stand for 10^-6)

Could someone please show me the steps to solving this?? i know what the correct answer is, but ineed to show how to solve for it.

Answer 1

Hint:

n = M / m

where

n - number of atoms
M - mass of the Earth
m - average mass of the atoms

But the average mass of the atoms is missing in your question. You wrote it is 40*10^(-6), but what units? Well, and also in the mass of the Earth is something missing. (M=5.98*10^24 kg.)

Maybe the average RELATIVE mass of the atoms should be 40? It seems quite realistic number. It corresponds to average mass of the atoms 6.64*10^(-26) kg.

Supposing that the average relative mass of the atoms is 40 we get this result:

n = (5.98*10^24 kg) / (6.64*10^(-26) kg) = 9 * 10^49

It means that 90 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 atoms are in the Earth.
-

Answer 2

Often overlooked in school is the fact that units of measure, like kg, meter, and sec, can be manipulated just like numbers or variables that represent numbers.

For example, if you have a mass M kg and a unit mass m kg/atom, getting the number of atoms n is simply a matter of noting that kg//kg/atom= atom. That is, we divide the mass M/m = n. And we do that because that's how the units of measure work out when treating them as numbers; that is, kg//kg/atom = M/m = n = atom.

Now you can just plug in the numbers. (BTW, I presumed your u was in kg/atom, but you did not specify that.)

Answer 3

number of atmos should be

No. of atmos = mass of earth / mass of 1 atom