Question

A radioactive material produces 1170 decays per minute at one time, and 4.8 h later produces 300 decays per minute.

Part A

What is its half-life?

Express your answer using two significant figures.

Part B

What is the activity of a sample of 146C that contains 2.8×10²⁰ nuclei?

Answer 1

A)
let Ro = 1170 decay/minute

at time t = 4.8 h, R = 300 decay/minute

let lamda is the decay constant

we know,

R = Ro*e^(-lamda*t)

R/Ro = e^(-lamda*t)

ln(R/Ro) = -lamda*t

==> lamda = ln(Ro/R)/t

= ln(1170/300)/4.8

= 0.283537 hour^-1

half life time, T1/2 = 0.693/lamda

= 0.693/0.283537

= 2.4 hours

B)

we half life of C, T1/2 = 5700 years

decay constant, lamda = 0.693/T1/2

= 0.693/(5700 years)

= 0.693/(5700*365*24*60*60)

= 3.86*10^-12 s^-1

we know, activity, A = lamda*N

= 3.86*10^-12*2.8*10^20

= 1.08*10^9 decay/second