Question

sample of radioactive element with initial mass 24 gm decay to 3 gm in 36 min how much of the original symbol remained after the first 12 min?​

Answer 1

Answer:

Mean Life =

λ

1

N

o

=10gms

First order decay:

N=N

o

e

−λt

At t=

λ

2

N=N

o

e

−2

=1.35 gms

Answer 2

Given info : sample of radioactive element with initial mass 24 gm decay to 3 gm in 36 min.

To find : the mass of sample remained after the first 12 min is ...

solution : initial mass of radioactive element, N₀ = 24 g

mass of radioactive after 36 min, N = 3 g

using formula, $N=N_0e^{-\lambda t}$

⇒3 = 24$e^{-\lambda 36}$

⇒ln8 = 36λ

⇒λ = ln8/36 = 3ln2/36 = ln2/12

now again using the same formula to find the mass of radioactive element remained after the first 12 min.

$N=N_0e^{-\lambda t}$

⇒N = 24$e^{-\frac{ln2}{12}\times 12}$

⇒N = 24$e^{-ln2}$ = 24 × 1/2 = 12g

Therefore 12g of radioactive element should be remained after the first 12 min.