Question

The radioactive decay of a certain sample produced 846 disintegrations per minute. exactly 3.00 days later, the rate of decay was found to be 269 disintegrations per minute. calculate the half-life, in days, for the decay of this sample.

Answer 1

`\boxed{\text{1.81 da}}`

Step-by-step explanation:

1. Calculate the decay constant

The integrated rate law for radioactive decay is 1

`\ln(A_(0))/(A_(t)) = kt`

where

A₀ and A_t are the counts at t = 0 and t

k is the radioactive decay constant

`\ln (846)/(269) = k * 3.00\\\\\ln3.145 = 3.00k\\1.146 = 3.00k\\\\k =(1.146)/(3)\\\\k = \text{0.382 /da}\\`

2. Calculate the half-life

`t_{(1)/(2)} = (\ln2)/(k) = (\ln2)/(0.382) = \text{1.81 da}`

The half-life for decay is
`\boxed{\textbf{1.81 da}}`.