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. Which has more atoms: a 1-g sample of carbon-12 or a
1-g sample of carbon-13? Explain

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Jimmy T. | Math, Chinese, GRE Math, Chemistry, PhysicsMath, Chinese, GRE Math, Chemistry, Phys...
The atomic nucleus contains a mix of positively charged protons and electrically neutral neutrons.  An atom is classified according to the number of protons and neutrons in its nucleus: the number of protons determines the chemical element, and the number of neutrons determines the isotope of the element. Over 99.94% of an atom's mass is concentrated in the nucleus,with protons and neutrons having roughly equal mass.
In the case of Carbon, one C-12 atom would have 6 protons and 6 neutrons, while one C-13 atom has 6 protons and 7 neutrons; they have the same number of neutrons so they are both identified as carbon, their neutron numbers are different, so they are isotopes of carbon.  As you may have noticed C-13 atom has one more neutron than C-12 atom, meaning it is one neutron heavier than C-12 atom. Given the equal-mass samples of C-12 and C-13, one can expect the C-12 sample to contain more atoms because C-12 atom is lighter than C-13 atom.
For more information, you can search for Carbon 12, Carbon 13, Isotope on WIKI
Hope this helps.