Q. 84.4( 5 Votes )
The normal activity of living carbon-containing matter is found to be about 15 decays per minute for every gram of carbon. This activity arises from the small proportion of radioactive 146C present with the stable carbon isotope 126C. When the organism is dead, its interaction with the atmosphere (which maintains the above equilibrium activity) ceases and its activity begins to drop. From the known half-life (5730 years) of 146C, and the measured activity, the age of the specimen can be approximately estimated. This is the principle of 146C dating used in archaeology. Suppose a specimen from Mohenjodaro gives an activity of 9 decays per minute per gram of carbon. Estimate the approximate age of the Indus-Valley civilization.
Let N be a number of radioactive carbon found in normal carbon and N0 be the number of radioactive carbon found in the specimen. The half-life of C-14 is 5730 yrs.
Decay rate of living carbon-containing matter = D = 15 decay/min-gm
Decay rate of the specimen at Mohenjo-Daro = D0 = 9 decays/min-gm
From the exponential decay rate law, we get,
So, -λt = ln(3/5) = -0.5108
or, t =
Approximate age of Indus-Valley-Civilization is 4223.5 years.
Rate this question :
A. A radioactive nucleus ‘A’ undergoes a series of decays as given below :
The mass number and atomic number of are 176 and 71 respectively. Determine the mass and atomic numbers of and A.
B. Write the basic nuclear processes underlying and decays.Physics - Board Papers
(a) Explain the processes of nuclear fission and nuclear fusion by using the plot of binding energy per nucleon (BE/A) versus the mass number A.
(b) A radioactive isotope has a half-life of 10 years. How long will it take for the activity to reduce to 3.125% ?Physics - Board Papers
Nuclei with magic no. of proton Z = 2, 8, 20, 28, 50, 52 and magic no. of neutrons N = 2, 8, 20, 28, 50, 82 and 126 are found to be very stable.
(i) Verify this by calculating the proton separation energy
Sp for 120Sn (Z = 50) and 121Sb = (Z = 51).
The proton separation energy for a nuclide is the minimum energy required to separate the least tightly bound proton from a nucleus of that nuclide. It is given by
Sp = (MZ–1, N + MH – MZ,N) c2.
Given 119In = 118.9058u, 120Sn = 119.902199u,
121Sb = 120.903824u, 1H = 1.0078252u.
(ii) What does the existence of magic number indicate?
Physics - Exemplar
The activity R of an unknown radioactive nuclide is measured at hourly intervals. The results found are tabulated as follows:
(i) Plot the graph of R versus t and calculate half-life from the graph.
(ii) Plot the graph of versus t and obtain the value of half-life from the graph.
Physics - Exemplar
Define the term ‘decay constant’ of a radioactive sample. The rate of disintegration of a given radioactive nucleus is 10000 disintegrations/s and 5,000 disintegrations/s after 20 hr. and 30 hr. respectively from start. Calculate the half life and initial number of nuclei at t = 0.Physics - Board Papers
(a) Write the relation between half-life and average life of a radioactive nucleus.
(b) In a given sample two isotopes A and B are initially present in the ratio of 1:2. Their half-lives are 60 years and 30 years respectively. How long will it take so that the sample has these isotopes in the ratio of 2:1?
Physics - Board Papers
A charged capacitor of capacitance C is discharged through a resistance R. A radioactive sample decays with an average-life τ. Find the value of R for which the ratio of the electrostatic field energy stored in the capacitor to the activity of the radioactive sample remains constant in time.HC Verma - Concepts of Physics Part 2
Sometimes a radioactive nucleus decays into a nucleus which itself is radioactive. An example is:
Assume that we start with 1000 38S nuclei at time t = 0. The number of 38Cl is of count zero at t = 0 and will again be zero at t = ∞. At what value of t, would the number of counts be a maximum?
Physics - Exemplar