Final answer:
To calculate the mass of cadmium atoms, we first determine the number of moles of cadmium using Avogadro's number. We then utilize the molar mass of cadmium to determine the mass in grams and convert that value to kilograms.
Step-by-step explanation:
To calculate the mass of a sample from the number of atoms, you need to consider the molar mass of the element and Avogadro's number. The Avogadro constant, commonly denoted NA or L, is an SI defining constant with an exact value of 6.02214076×1023 mol-1 (unit of reciprocal moles). It is used as a normalization factor in the amount of substance in a sample (in SI units of moles), defined as the number of constituent particles (usually molecules, atoms, or ions) divided by NA. In practice, its value is often approximated as 6.02×1023 mol-1 or 6.022×1023 mol-1.
The molar mass of Cadmium (Cd) is approximately 112.41 g/mol. Avogadro's number, which is the number of atoms in one mole, is 6.022 x 1023 atoms/mol. So, first, let's calculate the number of moles in the given number of atoms:
Moles of Cd = 3.19 x 1026 atoms / 6.022 x 1023 atoms/mol = 529.65 mol of Cd.
Now, we can calculate the mass in grams and then convert to kilograms:
Mass of Cd = 529.65 mol x 112.41 g/mol = 59548.94 g = 59548.94 Kg. Therefore, the sample of 3.19 x 1026 cadmium atoms would have a mass of 5.95 x 104Kg.
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