Advertisements
Advertisements
प्रश्न
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?
उत्तर
Given:-
Initial rate of decay, A0 = 500,
Rate of decay after 50 minutes, A = 200
Time, t = 50 min
= 50 × 60
= 3000 s
(a)
Activity, A = A0e−λt
Here, `lambda` = Disintegration constant
`therefore 200 = 500 xx e^(-50 xx 60 xx lambda)`
`⇒ 2/5 = e^(-3000lambda)`
`⇒ "In" 2/5 = -3000lambda`
`⇒ lambda = 3.05 xx 10^-4 "s"^-1`
(b)
Half - life, `T_"1/2" = 0.693/lambda`
`= 2272.13 "s"`
= 38 min
APPEARS IN
संबंधित प्रश्न
Write nuclear reaction equation for α-decay of `""_94^242"Pu"`.
Write nuclear reaction equation for β+-decay of `""_43^97"Tc"`.
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?
Radioactive 131I has a half-life of 8.0 days. A sample containing 131I has activity 20 µCi at t = 0. (a) What is its activity at t = 4 days? (b) What is its decay constant at t = 4.0 days?
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.
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?
`""_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.
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?
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?
In a gamma ray emission from nucleus :
The half-life of radium is 1550 years. Calculate its disintegration constant (`lambda`) .
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 ______.
