Question

Initial number of undecayed atoms in a radioactive sample is
1000. It is found that 100 atoms disintegrated in 2 hours. The
number of undecayed atoms in the sample after next 4 hours
will be
A. 700
B. 1
C. 810
D. 729​

Answer 1

Explanation:

Use equation of radioactive decay two times

Answer 2

Answer:

The number of undecayed atoms in the sample after the next 4 hours will be 729 i.e.option(D).

Explanation:

We will use the given relation to solve this question,

$N=N_0e^-^\lambda^t$        (1)

Where,

N=number of atoms left after the disintegration

N₀=initial number of atoms

λ=disintegration constant

t=time required for the disintegration of atoms

When t=2Hour

N₀=1000

N=1000-100=900

t=2 hour

By substituting the values in equation (1) we get;

$900=1000e^-^2^\lambda$

$e^-^2^\lambda=\frac{9}{10}$        (2)

When t=next 4 hour

t=2+4=6hour

By placing the values in equation (1) we get;

$N=1000\times e^-^6^\lambda$       (3)

By using equation (2) in equation (3) we get;

$N=1000\times (\frac{9}{10} )^3$

$N=729$

Hence, the number of undecayed atoms in the sample after the next 4 hours will be 729 i.e.option(D).