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

Half life is 3.23 hours

Step-by-step 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) = (ln2)/(\Lambda)`

Substituting the given values we get -

`t_(1/2) = =0.693/0.2085\\= 3.23`hours