Q. 184.2( 50 Votes )
The initial concentration of a radioactive substance is No and its half life is 12 hours. What will be its concentration after 36 hours?
In radioactive decay, nuclear half life expresses the time required for half of a sample to undergo radioactive decay.
Exponential decay can be expressed mathematically as
Where, N is concentration after t time, No is initial concentration,
t is time and is half life.
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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.NCERT - Physics Part-II
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
Radioactive isotopes are produced in a nuclear physics experiment at a constant rate dN/dt = R. An inductor of inductance 100 mH, a resistor of resistance 100 Ω and a battery are connected to form a series circuit. The circuit is switched on at the instant the production of radioactive isotope starts. It is found that i/N remains constant in time where i is the current in the circuit at time t and N is the number of active nuclei at time t. Find the half-life of the isotope.HC Verma - Concepts of Physics Part 2
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
A human body excretes (removes by waste discharge, sweating, etc.) certain materials by a law similar to radioactivity. If technetium is injected in some form in a human body, the body excretes half the amount in 24 hours. A patient is given an injection containing 99Tc. This isotope is radioactive with a half-life of 6 hours. The activity from the body just after the injection is 6 μCi. How much time will elapse before the activity falls to 3 μCi?HC Verma - Concepts of Physics Part 2
Define ‘half -life’ and ‘average-life’ of a radioactive substance. What is the relation between the two?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