Class 12 NEET Physics Atoms and Nuclei Questions Part 2

According to radioactive decay law
N=N0e−λt
where N0= Number of radioactive nuclei at time t=0
N = Number of radioactive nuclei left un decayed at any time t
λ= decay constant
At time t2,

2

3

of the sample had decayed
∴N=

1

3

N0
∴

1

3

N0=N0e−λt2.......(i)
At time t1,

1

3

of the sample had decayed
∴N=

2

3

N0
∴

2

3

N0=N0e−λt1.......(ii)
Divide (i) by (ii), we get

1

2

=

e−λt2

e−λt1

1

2

eλ(t2−t1)
λ(t2−t1)=ln2

=T

1

2

=50 days