Advertisements
Advertisements
प्रश्न
Consider the situation of the previous problem. Suppose the production of the radioactive isotope starts at t = 0. Find the number of active nuclei at time t.
Advertisements
उत्तर
Let the number of atoms present at t = 0 be N0.
Let N be the number of radio-active isotopes present at time t.
Then,
N = N0e−λt
Here, `lambda` = Disintegration constant
∴ Number of radioactive isotopes decayed = `N_0 - N = N_0 - N_0e^(-lambdat)`
= `N_0(1-e^(-lambdat))` ...(1)
Rate of decay (R) is given by
`R = lambdaN_0` ...(2)
Substituting the value of `N_0` from equation (2) to equation (1), we get
`N = N_0(1-e^(-lambdat))`
= `R/lambda (1 - e^(-lambdat))`
APPEARS IN
संबंधित प्रश्न
The decay constant of radioactive substance is 4.33 x 10-4 per year. Calculate its half life period.
State the law of radioactive decay.
Why is it found experimentally difficult to detect neutrinos in nuclear β-decay?
Under certain circumstances, a nucleus can decay by emitting a particle more massive than an α-particle. Consider the following decay processes:
\[\ce{^223_88Ra -> ^209_82Pb + ^14_6C}\]
\[\ce{^223_88 Ra -> ^219_86 Rn + ^4_2He}\]
Calculate the Q-values for these decays and determine that both are energetically allowed.
Using the equation `N = N_0e^(-lambdat)` obtain the relation between half-life (T) and decay constant (`lambda`) of a radioactive substance.
(a) Derive the relation between the decay constant and half life of a radioactive substance.
(b) A radioactive element reduces to 25% of its initial mass in 1000 years. Find its half life.
Two different radioactive elements with half lives T1 and T2 have N1 and N2 undecayed atoms respectively present at a given instant. Derive an expression for the ratio of their activities at this instant in terms of N1 and N2 ?
Why is it experimentally found difficult to detect neutrinos in this process ?
A radioactive nucleus ‘A’ undergoes a series of decays according to the following scheme:
The mass number and atomic number of A are 180 and 72 respectively. What are these numbers for A4?
The decay constant of 238U is 4.9 × 10−18 S−1. (a) What is the average-life of 238U? (b) What is the half-life of 238U? (c) By what factor does the activity of a 238U sample decrease in 9 × 109 years?
Obtain a relation between the half-life of a radioactive substance and decay constant (λ).
Identify the nature of the radioactive radiations emitted in each step of the decay process given below.
`""_Z^A X -> _Z^A _-1^-4 Y ->_Z^A _-1^-4 W`
A radioactive substance disintegrates into two types of daughter nuclei, one type with disintegration constant λ1 and the other type with disintegration constant λ2 . Determine the half-life of the radioactive substance.
What is the amount of \[\ce{_27^60Co}\] necessary to provide a radioactive source of strength 10.0 mCi, its half-life being 5.3 years?
Two radioactive materials X1 and X2 have decay constants 10λ and λ respectively. If initially, they have the same number of nuclei, then the ratio of the number of nuclei of X1 to that of X2 will belie after a time.
What percentage of radioactive substance is left after five half-lives?
The half-life of a radioactive nuclide is 20 hrs. The fraction of the original activity that will remain after 40 hrs is ______.
If 10% of a radioactive material decay in 5 days, then the amount of original material left after 20 days is approximately :
The variation of decay rate of two radioactive samples A and B with time is shown in figure.
Which of the following statements are true?
- Decay constant of A is greater than that of B, hence A always decays faster than B.
- Decay constant of B is greater than that of A but its decay rate is always smaller than that of A.
- Decay constant of A is greater than that of B but it does not always decay faster than B.
- Decay constant of B is smaller than that of A but still its decay rate becomes equal to that of A at a later instant.
What is the half-life period of a radioactive material if its activity drops to 1/16th of its initial value of 30 years?
