The diameter of a carbon atom is approximately 140 pm, whereas the diameter of a pencil lead is approximately 0.7 mm.How many carbon nuclei would be required to span 0.7 mm? The radius of the nucleus is approximately 10,000 times smaller than the radius of an atom.

Question

Quizplus · Accepted Answer

To find out how many carbon nuclei would span 0.7 mm, first convert the diameter of the pencil lead to picometers (pm) since the diameter of a carbon atom is given in pm. $0.7 \, \text{mm} = 700,000 \, \text{pm}$. Knowing the diameter of a carbon atom is 140 pm, the number of carbon atoms to span 0.7 mm is $700,000 \, \text{pm} / 140 \, \text{pm/atom} = 5,000,000 \, \text{atoms}$. Since the question asks for the number of nuclei and the nucleus is approximately 10,000 times smaller than the atom, this factor does not change the count of entities spanning the distance, thus the calculation directly applies to nuclei as well. Therefore, the correct answer is $5 \times 10^{6}$ nuclei.

The Diameter of a Carbon Atom Is Approximately 140 Pm