The mass of a single Barium atom is 2.28 times 10^{-22} grams. How many Barium atoms would there...

Question:

The mass of a single Barium atom is {eq}2.28 \times 10^{-22} {/eq} grams. How many Barium atoms would there be in {eq}37.4 {/eq} milligrams of Barium?

Atoms:

Atoms are stated to be the building blocks of matter. Atoms are normally made up of a nucleus, which in turn is made up of protons and neutrons. The number of protons dictate what element the atom is. Outside the nucleus, electrons orbit around the atom at discrete distances and energies.

Answer and Explanation:


Given:

  • {eq}\displaystyle m = 2.28\ \times\ 10^{-22}\ g {/eq} is the Ba atom mass
  • {eq}\displaystyle M = 37.4\ mg = 0.0374\ g {/eq} is the total mass of the Ba sample


If we want to know how many atoms of Ba there are, we can set n atoms with mass m to equal a mass M. We write this as:

{eq}\displaystyle M = nm {/eq}

We isolate n here:

{eq}\displaystyle n = \frac{M}{m} {/eq}

We substitute:

{eq}\displaystyle n = \frac{0.0374\ g}{2.28\ \times\ 10^{-22}\ g} {/eq}

We will get:

{eq}\displaystyle \boxed{n = 1.64\ \times\ 10^{20}} {/eq}


Learn more about this topic:

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