What is the mass of a 3.90-μCi 146C source? The half-life of 146C is 5730 yr.

As we know 1Ci = 3.7*10∧10 radiation which is per second.

N is number of atoms and if they are radiated it will be N * decay constant = 1Ci

⇒ N = 1 cl/decay constant = 3.7*10∧10/decay constant

Decay constant = ln (2) / half life = ln (2) / 5730 years.

= ln (2) / (5730*365*24*3600 seconds) = 3.8359*10∧ (-12)

Number of atoms = 3.5 * 10∧ (-6) * 3.7 * 10∧ 10 / (3.8359*10∧ (-12))

= 3.376 * 10∧ 16

∴ The number of moles = number of atoms / (6.022 * 10∧23)

= 5.6061 * 10∧ (-8)

mass = Molar mass * number of moles = 5.6061 * 10∧ (-8) * 14 grams

=7.8486 * 10∧ (-7) grams.