Question

A radioactive material is reduced to 1/16 of its original amount in four days. How much material should one begin with so that 4 * 10^-3 kg of the material is left after six days?

Answer 1

Hey User !

=) Radioactivity Decay Formula is given as

N=N0e-λt ---(1)Where,λ=Radioactivity Decay constantN0= Initial Amount of materialN=Material left after time t

Here, Given Data is

N=116N0 and t=4 days

Putting the values in Eq. (1) we get

16=e4λ⇒λ=ln164=ln2 ---(2)

Now in second case

Let the initial amount of material be M0 Kg

Given, N = 4 x 10-3 Kg

t = 6 days

Putting these values in Eq. (1), we get

4×10-3=M0e-6λPutting the value of λ from Eq. (2), we get4×10-3=M0e-6ln2⇒4×10-3=M0e-ln26⇒4×10-3=M0e-ln64=M064⇒M0 = 256 X 10-3 kg

Therefore, initial amount of material required is 256 x 10-3 Kg

Hope , It Helps ...