Question

A radioactive material is reduced to 1/16 of its original amount in 4 days how much material should one begin with so that 4*10

Answer 1

solution ;

radioactivity decay formula  is

N=Noe^-λt.....(1)

λ= radioactivity  Decay constant

Νo=initial  amount of material

Ν=material letf after t time

given data

Ν=1/16Νo t= 4 days

putting values in equation 1

16=e^4λ ⇒λ=In 16/4=In 2...(2)

now second case

let initial  amount of material Mo Kg

given Ν=4*10^-3 kg t= 6 days

 putting values in 1

4*10^-3=Moe^-6λ          o=256 *10^-3kg

putting λin equation 2

4*10^-3=Moe^-6In2    

⇒4*10^-3=Moe^-In2^6    

⇒4*10^-3=Moe^-In64=  Mo/64

⇒M

so initial amount  required 256*10^-3 kg