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.

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