Advertisements
Advertisements
प्रश्न
In an agricultural experiment, a solution containing 1 mole of a radioactive material (t1/2= 14.3 days) was injected into the roots of a plant. The plant was allowed 70 hours to settle down and then activity was measured in its fruit. If the activity measured was 1 µCi, what per cent of activity is transmitted from the root to the fruit in steady state?
उत्तर
Given:
Initial no of atoms, N0 = 1 mole = 6 × 1023 atoms
Half-life of the radioactive material, T1/2 = 14.3 days
Time taken by the plant to settle down, t = 70 h
Disintegration constant, `lambda = 0.693/t_"1/2"` = `0.693/(14.3 xx 24) "h"^-1`
`N = N_0e^(-lambdat)`
= `6 xx 10^23 xx e^((-0.693 xx 70)/(14.3 xx 24))`
= `6 xx 10^23 xx 0.868`
= `5.209 xx 10^23`
Activity , `R = "dN"/"dt" = 5.209 xx 10^23 xx 0.693/(14.3 xx 24)`
= `(0.0105 xx 10^23)/3600 "dis/hr"`
= `2.9 xx 10^-6 xx 10^23 "dis/sec"`
= `2.9 xx 10^17 "dis/sec"`
Fraction of activity transmitted = `((1 µCi)/(2.9 xx 10^17)) xx 100%`
= `[((1 xx 3.7 xx 10^4)/(2.9 xx 10^17)) xx 100%]`
= `1.275 xx 10^-11 %`
APPEARS IN
संबंधित प्रश्न
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?
State the law of radioactive decay. hence derive the relation N = Noe-λt . Represent it graphically.
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.
`""_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.
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.
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.
Natural water contains a small amount of tritium (`""_1^3H`). This isotope beta-decays with a half-life of 12.5 years. A mountaineer while climbing towards a difficult peak finds debris of some earlier unsuccessful attempt. Among other things he finds a sealed bottled of whisky. On returning, he analyses the whisky and finds that it contains only 1.5 per cent of the `""_1^3H` radioactivity as compared to a recently purchased bottle marked '8 years old'. Estimate the time of that unsuccessful attempt.
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?
`""_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?
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.
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`
The half-life of a certain radioactive element is 3.465 days. Find its disintegration constant.
Half-life of a certain radioactive material is 8 hours.
Find the disintegration constant of this material.
Half life of a certain radioactive material is 8 hours.
If one starts with 600 g of this substance, how much of it will disintegrate in one day?
