Question

A radioactive material produces 1160 decays per minute at one time, and 4.0 h later produces 170 decays per minute. whats the half life

Answer 1

Answer:

Half life is 3.23 hours

Explanation:

Given

Decay rate at starting = 1160 decays per minute

Decay rate after 4 hours = 170 decays per minute

As we know know

$N = N_0 *e ^{\Lambda *T}$

Substituting the given values, we get -

$170 = 1160 *e ^{-4*\Lambda}\\0.1465 = e ^{-4*\Lambda}\\-0.834 = -4 * \Lambda\\\Lambda = 0.834/4\\\Lambda = 0.2085$

Also

$t_{1/2} = \frac{ln2}{\Lambda}$

Substituting the given values we get -

$t_{1/2} = =0.693/0.2085\\= 3.23$hours