Question

What is the mass of a 4.50-μci 146c source? the half-life of 146c is 5730 yr.

express your answer to three significant figures and include the appropriate units?

Answer 1

The activity of the sample is:
R₀ = 4.5 x 10⁻⁶ Ci (3.70 x 10¹⁰ decays/s / 1 Ci)
= 166500 decays / s

The number of nuclei is:
N₀ = (166500 decays/s) / (5730 yr * 3.154 x 10⁷s /1yr) = 9.2 x 10⁻⁷

The mass of a ₆C¹⁴ source is:
m = N₀m₀ = (9.2 x 10⁻⁷) * (2.34 x 10⁻²⁶) = 2.16 x 10⁻³² kg