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
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 α-decay of `""_88^226"Ra"`.
Write nuclear reaction equation for electron capture of `""_54^120"Xe"`.
A radioactive nucleus has a decay constant λ = 0.3465 (day)–1. How long would it take the nucleus to decay to 75% of its initial amount?
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 199Au is 2.7 days. (a) Find the activity of a sample containing 1.00 µg of 198Au. (b) What will be the activity after 7 days? Take the atomic weight of 198Au to be 198 g mol−1.
The count rate from a radioactive sample falls from 4.0 × 106 per second to 1.0 × 106per second in 20 hours. What will be the count rate 100 hours after the beginning?
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.
The count rate of nuclear radiation coming from a radiation coming from a radioactive sample containing 128I varies with time as follows.
| Time t (minute): | 0 | 25 | 50 | 75 | 100 |
| Ctount rate R (109 s−1): | 30 | 16 | 8.0 | 3.8 | 2.0 |
(a) Plot In (R0/R) against t. (b) From the slope of the best straight line through the points, find the decay constant λ. (c) Calculate the half-life t1/2.
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.
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.
`""_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?
In a gamma ray emission from nucleus :
The half-life of radium is 1550 years. Calculate its disintegration constant (`lambda`) .
Complete the following nuclear reactions :
(i) `"_15^32P -> ` `"_z^AX + bar(e) + bar(v)`
(ii) `"_6^12 C `+`"_6^12C ->` ` "_2^A Y + ` `"_4^2 He`
A radioactive substance decays to 1/16th of its initial mass in 40 days. The half-life of the substance, in days, is:
The half-life of a certain radioactive element is 3.465 days. Find its disintegration constant.
A nucleus with Z = 92 emits the following in a sequence:
α, β‾, β‾, α, α, α, α, α, β‾, β‾, α, β+, β+, α
Then Z of the resulting nucleus is ______.
