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

Answer:

$\boxed{\text{1.81 da}}$

Explanation:

1. Calculate the decay constant

The integrated rate law for radioactive decay is 1

$\ln\dfrac{A_{0}}{A_{t}} = kt$

where

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

k is the radioactive decay constant

$\ln \dfrac{846}{269} = k \times 3.00\\\\\ln3.145 = 3.00k\\1.146 = 3.00k\\\\k =\dfrac{1.146}{3}\\\\k = \text{0.382 /da}$

2. Calculate the half-life

$t_{\frac{1}{2}} = \dfrac{\ln2}{k} = \dfrac{\ln2}{0.382} = \text{1.81 da}$

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