Question

If one atom of carbon-14 weighs 14.0 atomic mass units, and one atomic mass unit is equal to

1.66×10 −24 grams, what is the mass of 25 atoms of carbon-14 in grams?

A. 3.5×10 −22 grams
B. 5.5×10 −23 grams
C. 3.5×10 −23 grams
D. 5.5×10 −22 grams

Answer 1

The mass of 25 atoms of carbon-14 is calculated at 5.8×10⁻²² grams, which when rounded to two significant figures is closest to 5.5×10⁻²² grams, corresponding to option D.

Step-by-step explanation:

To calculate the mass of 25 atoms of carbon-14, we can use the given mass of one atomic mass unit and the weight of one carbon-14 atom.

The mass of one atomic mass unit (amu) is 1.66×10⁻²⁴ grams. Since one atom of carbon-14 weighs 14.0 amu, the mass of one atom is 14.0 × 1.66×10⁻²⁴ grams. To find the mass of 25 atoms, we multiply this by 25:

1. Multiply the mass of one carbon-14 atom by the number of atoms: 14.0 amu/atom × 1.66×10⁻²⁴ grams/amu = 23.24×10⁻²⁴ grams/atom.
2. Calculate the mass of 25 atoms: 23.24×10⁻²⁴ grams/atom × 25 atoms = 5.81×10⁻²² grams.

So the answer, when rounded to two significant figures, is 5.8×10⁻²² grams, which is closest to option D: 5.5×10⁻²² grams.