[reemie]

The answer according to my booklet is 1.6734×10^-24 (g), but I don't understand how we got this answer.

proton: 1.6725×10^-24
neutron: 1.6748×10^-24
electron: 0.0009×10^-24

To get the mass, I added protons with neutrons, but I got 3.3473×10^-24.

What am I doing wrong?

[cseil]

I suppose you're considering the most abundant isotope.
A hydrogen atom doesn't have a neutron. But even if you don't consider the neutron but only the proton you get a different answer. Why?

[reemie]

I didn't realize that hydrogen doesn't have any neutrons. But if we subtract the number of protons from the answer, we get 9x10^-28, and I can't figure out where this number came from.

[cseil]

You have this number in your list, don't you?
It's the electron!

[reemie]

Oh, that's right! But why did we add the electrons and the protons to get the mass? Isn't the mass the sum of protons and neutrons? do I have to add all the three particles for every element too to get the mass?

[Borek]

Isn't the mass the sum of protons and neutrons?

That would yield mass of the nucleus*, not the atom.

*Actually it wouldn't, mass of the nucleus is always lower than the sum of masses of neutrons and protons, with a sole exception of ¹H - the lightest hydrogen isotope. Google "mass defect" if you are interested in details.