Advertisements
Advertisements
प्रश्न
The selling rate of a radioactive isotope is decided by its activity. What will be the second-hand rate of a one month old 32P(t1/2 = 14.3 days) source if it was originally purchased for 800 rupees?
उत्तर
Given:
Half-life of 32P source, `T_(1"/"2)`= 14.3 days
Time, t = 30 days = 1 month
Here, the selling rate of a radioactive isotope is decided by its activity.
∴ Selling rate = Activity of the radioactive isotope after 1 month
Initial activity, A0 = 800 disintegration/sec
Disintegration constant (`lambda`) is given by
`lambda = 0.693/T_(1"/"2) = 0.693/14.3 "days"^-1`
Activity (A) is given by
`A = A_0e^(-lambdat)`
Here, `lambda` = Disintegration constant
`therefore` Activity of the radioactive isotope after one month (selling rate of the radioactive isotope) (A) is given below .
`A = 800 xx e^(-0.693/14.3) xx 30`
= `800 xx 0.233669`
= 186.935 = Rs 187
APPEARS IN
संबंधित प्रश्न
For the past some time, Aarti had been observing some erratic body movement, unsteadiness and lack of coordination in the activities of her sister Radha, who also used to complain of severe headache occasionally. Aarti suggested to her parents to get a medical check-up of Radha. The doctor thoroughly examined Radha and diagnosed that she has a brain tumour.
(a) What, according to you, are the values displayed by Aarti?
(b) How can radioisotopes help a doctor to diagnose brain tumour?
Write nuclear reaction equation for α-decay of `""_88^226"Ra"`.
Write nuclear reaction equation for α-decay of `""_94^242"Pu"`.
Write nuclear reaction equation for β−-decay of `""_83^210"Bi"`.
Write nuclear reaction equation for β+-decay of `""_43^97"Tc"`.
Draw graphs showing variation of photoelectric current with applied voltage for two incident radiations of equal frequency and different intensities. Mark the graph for the radiation of higher intensity.
Plot a graph showing variation of activity of a given radioactive sample with time.
The sequence of stepwise decay of a radioactive nucleus is
If the atomic number and mass number of D2 are 71 and 176 respectively, what are their corresponding values of D?
The half-life of 226Ra is 1602 y. Calculate the activity of 0.1 g of RaCl2 in which all the radium is in the form of 226Ra. Taken atomic weight of Ra to be 226 g mol−1 and that of Cl to be 35.5 g mol−1.
`""_80^197`Hg decay to `""_79^197`Au through electron capture with a decay constant of 0.257 per day. (a) What other particle or particles are emitted in the decay? (b) Assume that the electron is captured from the K shell. Use Moseley's law √v = a(Z − b) with a = 4.95 × 107s−1/2 and b = 1 to find the wavelength of the Kα X-ray emitted following the electron capture.
4 × 1023 tritium atoms are contained in a vessel. The half-life of decay tritium nuclei is 12.3 y. Find (a) the activity of the sample, (b) the number of decay in the next 10 hours (c) the number of decays in the next 6.15 y.
238U decays to 206Pb with a half-life of 4.47 × 109 y. This happens in a number of steps. Can you justify a single half for this chain of processes? A sample of rock is found to contain 2.00 mg of 238U and 0.600 mg of 206Pb. Assuming that all the lead has come from uranium, find the life of the rock.
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?
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.
Plot a graph showing the variation of undecayed nuclei N versus time t. From the graph, find out how one can determine the half-life and average life of the radioactive nuclei.
The half-life of a certain radioactive element is 3.465 days. Find its disintegration constant.
