Final answer:
To find the relative atomic mass of argon, divide the mass of one argon atom (6.64 × 10⁻²⁶ kg) by the mass of one atomic mass unit (1.67 × 10⁻²⁷ kg). The result is approximately 40 u, which matches option (a) and is equivalent to the standard molar mass of argon.
Step-by-step explanation:
The student's question asks for the calculation of the relative atomic mass of argon when one atom of argon has a mass of 6.64 × 10⁻²⁶ kg. The relative atomic mass of an element is dimensionless and is the ratio of the average mass per atom of the element to 1/12 of the mass of carbon-12. This value is approximately equivalent to the molar mass of the element in grams per mole.
Using the value of 1 atomic mass unit (u) which is 1.67 × 10⁻²⁷ kg, we can convert the mass of one argon atom to atomic mass units by dividing the given atomic mass by the value of 1 atomic mass unit:
Argon atomic mass =
(6.64 × 10⁻²⁶ kg) / (1.67 × 10⁻²⁷ kg/u) = 39.76 u
When we round this value to the nearest whole number, as is customary for relative atomic masses, we get 40 u, which corresponds to option (a). This is consistent with the molar mass of argon from the periodic table, which is approximately 39.948 g/mol, often rounded to 40 g/mol for general calculations.