Question

Q8 A radioactive isotopes has a half life of 49 years. Find the time taken by the isotope so that its activity is reduced to 1% of its original value?​

Answer 1

Answer:

Thus, the isotope will take about 5T years to reduce to 3.125% of its original value. Hence, the isotope will take about 6.645Tyears to reduce to 1% of its original value.

Explanation:

(a) Let the half-life be T years.

original amount of isotope is N

o

after decay, the remaining amount is N

now as per given values, N/N

o

=3.125%=1/32

also, N/N

o

=e

−λt

where λ is decay constant

also λ=0.693/T

so, t=3.4657/λ=5T years.

(b) Let the half-life be T years.

original amount of isotope is N

o

after decay, the remaining amount is N

now as per given values, N/N

o

=1%=1/100

also, N/N

o

=e

−λt

where λ is decay constant

also λ=0.693/T

so, t=4.6052/λ=6.645T years.