Nuclear Physics and RadioactivityHard
Question
The activity of radio active sample is measured as N0 counts per minute at t = 0 and N0 /e counts per minute at t = 5 minute. The time (in minutes) at which the activity reduces to half its value is
Options
A.loge
B.
C.5 log102
D.5 loge2
Solution
According to activity law
R = R0e-λt .....(i)
where,
R0 = initial activity at t = 0
R = activity at time t
λ = decay constant
According to given problem
R0 = N0 counts per minute
R =
counts per minute
t = 5 minute
Substituting these values in equation (i), we get
= N0e-5λ
e-1 = e-5λ
5λ = 1 or λ =
per minute
At t = T1/2 the activity reduces to
where T1/2 = half life of a radioactive sample
From equation (i), we get
= R0e-λT1/2
e-λT1/2 = 2
Taking natural logarithms of both sides above equation, we get
λT1/2 = loge2
or T1/2
= 5loge 2 minutes
R = R0e-λt .....(i)
where,
R0 = initial activity at t = 0
R = activity at time t
λ = decay constant
According to given problem
R0 = N0 counts per minute
R =
counts per minutet = 5 minute
Substituting these values in equation (i), we get
= N0e-5λe-1 = e-5λ
5λ = 1 or λ =
per minuteAt t = T1/2 the activity reduces to
where T1/2 = half life of a radioactive sample
From equation (i), we get
= R0e-λT1/2 e-λT1/2 = 2
Taking natural logarithms of both sides above equation, we get
λT1/2 = loge2
or T1/2
= 5loge 2 minutesCreate a free account to view solution
View Solution FreeMore Nuclear Physics and Radioactivity Questions
The capacity of Tarapur Atomic Power Station is 200 MW. The energy produced at this station in one day will be :-...Four statements are given ( $A$ is mass number):A. The volume of a nucleus is proportional to $A^{1/3}$.B. The volume of...Let Fpp, Fpn and Fnn denote the nuclear force between proton - proton, proton-neutron and neutron -neutron pair respecti...The electron emitted in beta radiation originates from:...In a photoelectric experiment, with light of wavelength λ the fastest electron has speed v. If the wavelength is ch...