The mass number of an atom is the sum of the number of protons and neutrons in its nucleus. It is represented by the formula:
\[ \text{Mass Number} = \text{Number of Protons} + \text{Number of Neutrons} \]
For a neutral atom, the number of electrons is equal to the number of protons. Given that the atom has 35 electrons, it also has 35 protons.
Using the formula from Step 1, we can calculate the mass number:
\[ \text{Mass Number} = 35 \, (\text{protons}) + 38 \, (\text{neutrons}) = 73 \]
The mass number of the atom is \(\boxed{73}\).
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