Final answer:
None of the provided options is correct for the mass of radon present given 3.5 x 10⁵ atoms. By converting the number of atoms to moles and then to kilograms using Avogadro's number and the molar mass of radon, the result is 12,900 kg of radon.
Step-by-step explanation:
To determine the mass of radon in kilograms when given the number of atoms, we use Avogadro's number and the molar mass of radon. There are 3.5 x 10⁵ atoms of radon (Rn), and Avogadro's number is 6.022 x 10²³ atoms/mol. The molar mass of radon (Rn-222) is approximately 222 g/mol.
First, we convert the number of atoms to moles using Avogadro's number:
3.5 x 10⁵ atoms Rn x (1 mol Rn / 6.022 x 10²³ atoms Rn) = 5.81 x 10² moles Rn
Next, we convert moles to grams using the molar mass of radon:
5.81 x 10² moles Rn x (222 g/mol Rn) = 1.29 x 10⁵ grams Rn
Finally, we convert grams to kilograms:
1.29 x 10⁵ grams Rn x (1 kg / 1000 g) = 12,900 kg Rn
Therefore, the correct answer is none of the provided options, as the calculation shows there are 12,900 kg of radon, which is not listed in the answer choices.