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प्रश्न
Represent Radioactive Decay curve using relation `N = N_o e^(-lambdat)` graphically
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उत्तर
Decay curve:
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संबंधित प्रश्न
State the law of radioactive decay.
Obtain the relation between the decay constant and half life of a radioactive sample.
Write symbolically the process expressing the β+ decay of `""_11^22Na`. Also write the basic nuclear process underlying this decay.
Why is it found experimentally difficult to detect neutrinos in nuclear β-decay?
A radioactive isotope has a half-life of T years. How long will it take the activity to reduce to a) 3.125%, b) 1% of its original value?
The normal activity of living carbon-containing matter is found to be about 15 decays per minute for every gram of carbon. This activity arises from the small proportion of radioactive `""_6^14"C"` present with the stable carbon isotope `""_6^12"C"`. When the organism is dead, its interaction with the atmosphere (which maintains the above equilibrium activity) ceases and its activity begins to drop. From the known half-life (5730 years) of `""_6^14"C"` and the measured activity, the age of the specimen can be approximately estimated. This is the principle of `""_6^14"C"` dating used in archaeology. Suppose a specimen from Mohenjodaro gives an activity of 9 decays per minute per gram of carbon. Estimate the approximate age of the Indus-Valley civilisation.
The half-life of `""_38^90 "Sr"` is 28 years. What is the disintegration rate of 15 mg of this isotope?
The radionuclide 11C decays according to
\[\ce{^11_6C -> ^11_5B + e+ + \text{v}}\] : T1/2 = 20.3 min
The maximum energy of the emitted positron is 0.960 MeV.
Given the mass values: `"m"(""_6^11"C") = 11.011434 u and "m"(""_6^11"B") = 11.009305 "u"`
Calculate Q and compare it with the maximum energy of the positron emitted.
A source contains two phosphorous radio nuclides `""_15^32"P"` (T1/2 = 14.3d) and `""_15^33"P"` (T1/2 = 25.3d). Initially, 10% of the decays come from `""_15^33"P"`. How long one must wait until 90% do so?
A radioactive nucleus 'A' undergoes a series of decays as given below:
The mass number and atomic number of A2 are 176 and 71 respectively. Determine the mass and atomic numbers of A4 and A.
Define 'activity' of a radioactive substance ?
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 ?
Define the activity of a given radioactive substance. Write its S.I. unit.
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 radioactive isotope D decays according to the sequence
If the mass number and atomic number of D2 are 176 and 71 respectively, what is (i) the mass number (ii) atomic number of D?
In a radioactive decay, neither the atomic number nor the mass number changes. Which of the following particles is emitted in the decay?
Lithium (Z = 3) has two stable isotopes 6Li and 7Li. When neutrons are bombarded on lithium sample, electrons and α-particles are ejected. Write down the nuclear process taking place.
The masses of 11C and 11B are respectively 11.0114 u and 11.0093 u. Find the maximum energy a positron can have in the β*-decay of 11C to 11B.
(Use Mass of proton mp = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron mn = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c2,1 u = 931 MeV/c2.)
28Th emits an alpha particle to reduce to 224Ra. Calculate the kinetic energy of the alpha particle emitted in the following decay:
`""^228"Th" → ""^224"Ra"^(∗) + alpha`
`""^224"Ra"^(∗) → ""^224"Ra" + γ (217 "keV")`.
Atomic mass of 228Th is 228.028726 u, that of 224Ra is 224.020196 u and that of `""_2^4H` is 4.00260 u.
(Use Mass of proton mp = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron mn = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c2,1 u = 931 MeV/c2.)
The decay constant of `""_80^197`Hg (electron capture to `""_79^197`Au) is 1.8 × 10−4 S−1. (a) What is the half-life? (b) What is the average-life? (c) How much time will it take to convert 25% of this isotope of mercury into gold?
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?
57Co decays to 57Fe by β+- emission. The resulting 57Fe is in its excited state and comes to the ground state by emitting γ-rays. The half-life of β+- decay is 270 days and that of the γ-emissions is 10−8 s. A sample of 57Co gives 5.0 × 109 gamma rays per second. How much time will elapse before the emission rate of gamma rays drops to 2.5 × 109per second?
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.
Define the term 'decay constant' of a radioactive sample. The rate of disintegration of a given radioactive nucleus is 10000 disintegrations/s and 5,000 disintegrations/s after 20 hr. and 30 hr. respectively from start. Calculate the half-life and the initial number of nuclei at t= 0.
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?
A source contains two species of phosphorous nuclei, \[\ce{_15^32P}\] (T1/2 = 14.3 d) and \[\ce{_15^33P}\] (T1/2 = 25.3 d). At time t = 0, 90% of the decays are from \[\ce{_15^32P}\]. How much time has to elapse for only 15% of the decays to be from \[\ce{_15^32P}\]?
Obtain an expression for the decay law of radioactivity. Hence show that the activity A(t) =λNO e-λt.
A radioactive element disintegrates for an interval of time equal to its mean lifetime. The fraction that has disintegrated is ______
Which one of the following nuclei has shorter meant life?
The half-life of a radioactive sample undergoing `alpha` - decay is 1.4 x 1017 s. If the number of nuclei in the sample is 2.0 x 1021, the activity of the sample is nearly ____________.
After 1 hour, `(1/8)^"th"` of the initial mass of a certain radioactive isotope remains undecayed. The half-life of the isotopes is ______.
Two radioactive materials Y1 and Y2 have decay constants '5`lambda`' and `lambda` respectively. Initially they have same number of nuclei. After time 't', the ratio of number of nuclei of Y1 to that of Y2 is `1/"e"`, then 't' is equal to ______.
The half-life of a radioactive nuclide is 20 hrs. The fraction of the original activity that will remain after 40 hrs is ______.
The half-life of the radioactive substance is 40 days. The substance will disintegrate completely in
When a nucleus in an atom undergoes a radioactive decay, the electronic energy levels of the atom ______.
Samples of two radioactive nuclides A and B are taken. λA and λB are the disintegration constants of A and B respectively. In which of the following cases, the two samples can simultaneously have the same decay rate at any time?
- Initial rate of decay of A is twice the initial rate of decay of B and λA = λB.
- Initial rate of decay of A is twice the initial rate of decay of B and λA > λB.
- Initial rate of decay of B is twice the initial rate of decay of A and λA > λB.
- Initial rate of decay of B is the same as the rate of decay of A at t = 2h and λB < λA.
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.
A piece of wood from the ruins of an ancient building was found to have a 14C activity of 12 disintegrations per minute per gram of its carbon content. The 14C activity of the living wood is 16 disintegrations per minute per gram. How long ago did the tree, from which the wooden sample came, die? Given half-life of 14C is 5760 years.
The activity R of an unknown radioactive nuclide is measured at hourly intervals. The results found are tabulated as follows:
| t (h) | 0 | 1 | 2 | 3 | 4 |
| R (MBq) | 100 | 35.36 | 12.51 | 4.42 | 1.56 |
- Plot the graph of R versus t and calculate the half-life from the graph.
- Plot the graph of ln `(R/R_0)` versus t and obtain the value of half-life from the graph.
The radioactivity of an old sample of whisky due to tritium (half-life 12.5 years) was found to be only about 4% of that measured in a recently purchased bottle marked 10 years old. The age of a sample is ______ years.
What is the half-life period of a radioactive material if its activity drops to 1/16th of its initial value of 30 years?
In the uranium radioactive series, the initial nucleus is \[\ce{_92U^238}\] and that the final nucleus is \[\ce{_82U^206}\]. When uranium nucleus decays to lead, the number of α particles and β particles emitted are ______.
