Advertisements
Advertisements
प्रश्न
`""_83^212"Bi"` can disintegrate either by emitting an α-particle of by emitting a β−-particle. (a) Write the two equations showing the products of the decays. (b) The probabilities of disintegration α-and β-decays are in the ratio 7/13. The overall half-life of 212Bi is one hour. If 1 g of pure 212Bi is taken at 12.00 noon, what will be the composition of this sample at 1 P.m. the same day?
उत्तर
Given:-
Half-life of `""^212"Bi" , T_"1/2" = 1 "h"^-1`
When `""_83^212"Bi"` disintegrates by emitting an α-particle
`""_83^212"Bi" → ""_81^208"T1" + ""_2^4"He"(alpha)`
When `""_83^212"Bi"` disintegrates by emitting a β−particle
`""_83^212"Bi" → ""_84^212P_0 + β^(-)+ bar"v"`
Half-life period of 212Bi, `T_(1/2)`= 1 `"h"^-1`
At t = 0, the amount of 212Bi present = 1 g
At t = 1 = One half-life,
Amount of 212Bi present = 0.5 g
Probability of disintegration of α-decay and β-decay are in the ratio `7/13`.
In 20 g of 212Bi, the amount of 208Ti formed = 7 g
In 1 g of 212Bi, the amount of 208Ti formed = 7/20 g
∴ Amount of `""^208"Ti"` present in `0.5 "g" = 7/20 xx 0.5 = 0.175 "g"`
In 20 g of 212Bi, the amount of 212Po formed = 13 g
In 1 g of 212Bi, the amount of 212Po formed = 13/20 g
∴ Amount of `""^212"Po"` present in `0.5 "g" = 13/20 xx 0.5 = 0.325 "g"`
APPEARS IN
संबंधित प्रश्न
The half life of a certain radioactive material against \u0003α-decay is 100 days. After how much time, will the undecayed fraction of the material be 6.25%?
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 β−-decay of `""_15^32"P"`.
Write nuclear reaction equation for electron capture of `""_54^120"Xe"`.
Plot a graph showing variation of activity of a given radioactive sample with time.
State the law of radioactive decay. hence derive the relation N = Noe-λt . Represent it graphically.
A certain sample of a radioactive material decays at the rate of 500 per second at a certain time. The count rate falls to 200 per second after 50 minutes. (a) What is the decay constant of the sample? (b) What is its half-life?
The half-life of a radioisotope is 10 h. Find the total number of disintegration in the tenth hour measured from a time when the activity was 1 Ci.
A vessel of volume 125 cm3 contains tritium (3H, t1/2 = 12.3 y) at 500 kPa and 300 K. Calculate the activity of the gas.
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?
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.
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.
A sample contains a mixture of 108Ag and 110Ag isotopes each having an activity of 8.0 × 108 disintegration per second. 110Ag is known to have larger half-life than 108Ag. The activity A is measured as a function of time and the following data are obtained.
| Time (s) |
Activity (A) (108 disinte- grations s−1) |
Time (s) |
Activity (A 108 disinte-grations s−1) |
| 20 40 60 80 100 |
11.799 9.1680 7.4492 6.2684 5.4115 |
200 300 400 500 |
3.0828 1.8899 1.1671 0.7212 |
(a) Plot ln (A/A0) versus time. (b) See that for large values of time, the plot is nearly linear. Deduce the half-life of 110Ag from this portion of the plot. (c) Use the half-life of 110Ag to calculate the activity corresponding to 108Ag in the first 50 s. (d) Plot In (A/A0) versus time for 108Ag for the first 50 s. (e) Find the half-life of 108Ag.
The half-life of radium is 1550 years. Calculate its disintegration constant (`lambda`) .
Copy and complete the following table for a radioactive element whose half-life is 10 minutes. Assume that you have 30g of this element at t = 0.
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.
