A mole (Avogadros number) is the number that is equivalent to the number of atoms in 12 grams of pure carbon-12, which is always 6.022 x 10²³ atoms.

Hydrogen has an atomic weight of 1.0079 rather than 1.0000 because a small proportion of hydrogen atoms are the isotope deuterium, or hydrogen-2, which has one proton and one neutron rather than just one proton. An even smaller proportion of hydrogen atoms are the isotope tritium, or hydrogen-3, which has one proton and two neutrons. These isotopes with an additional neutron add a tiny amount to hydrogens average atomic weight.

The atomic weight of hydrogen is 1.0079, which means that one mole of hydrogen atoms (or 6.0221 x 10²³ atoms of hydrogen) has a mass of 1.0079 grams. So, if there is 1.0079 grams of hydrogen per mole, then you can find out the number of hydrogen atoms in 1.0000 grams using the following proportion:
6.0221 x 10²³ atoms H / 1.0079 g H = x atoms H / 1.0000 g H

Multiply both sides of the equation by 1.0 g H to isolate the variable x on the right side.
1.0000 g H * (6.022 x 10²³ atoms H / 1.0079 g H) = x atoms H

Simplify and cancel terms.
6.0221 x 10²³ atoms H / 1.0079 = x atoms H

Multiply and round the answer to 5 significant figures.
5.9749 x 10²³ atoms H / 1.0000 g H

Because the molecular mass of Hydrogen is 1 gram/mole, there is 1 mole of hydrogen in 1 gram of hydrogen atoms. For every mole, there are 6.02*10²³ atoms, so in 1 gram of hydrogen there are 6.02*10²³ hydrogen atoms (in scientific notation) this is equal to 602000000000000000000000 hydrogen atoms.

Hydrogen has an atomic mass of 1.01 atomic mass units. An atomic mass unit is TINY. One gram is equal to about 602000000000000000000000 amu (or 6 followed by 23 zeros). So, because the mass of hydrogen is close to 1 amu (atomic mass unit),1 gram of hydrogen contains about that same huge number of atoms.