Advertisements
Advertisements
प्रश्न
Represent Radioactive Decay curve using relation `N = N_o e^(-lambdat)` graphically
Advertisements
उत्तर
Decay curve:
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.
How is the mean life of a given radioactive nucleus related to the decay constant?
Obtain the relation between the decay constant and half life of a radioactive sample.
Why is it found experimentally difficult to detect neutrinos in nuclear β-decay?
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.
Obtain the amount of `""_27^60"Co"` necessary to provide a radioactive source of 8.0 mCi strength. The half-life of `""_27^60"Co"` is 5.3 years.
The half-life of `""_38^90 "Sr"` is 28 years. What is the disintegration rate of 15 mg of this isotope?
The Q value of a nuclear reaction A + b → C + d is defined by
Q = [mA+ mb − mC − md]c2 where the masses refer to the respective nuclei. Determine from the given data the Q-value of the following reactions and state whether the reactions are exothermic or endothermic.
\[\ce{^12_6C + ^12_6C ->^20_10Ne + ^4_2He}\]
Atomic masses are given to be
`"m"(""_1^2"H")` = 2.014102 u
`"m"(""_1^3"H")` = 3.016049 u
`"m"(""_6^12C)` = 12.000000 u
`"m"(""_10^20"Ne")` = 19.992439 u
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?
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.
(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.
Define 'activity' of a radioactive substance ?
Why is it experimentally found difficult to detect neutrinos in this process ?
In a given sample, two radioisotopes, A and B, are initially present in the ration of 1 : 4. The half lives of A and B are respectively 100 years and 50 years. Find the time after which the amounts of A and B become equal.
In a radioactive decay, neither the atomic number nor the mass number changes. Which of the following particles is emitted in the decay?
A freshly prepared radioactive source of half-life 2 h emits radiation of intensity which is 64 times the permissible safe level. The minimum time after which it would be possible to work safely with this source is
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.
Calculate the maximum kinetic energy of the beta particle emitted in the following decay scheme:
12N → 12C* + e+ + v
12C* → 12C + γ (4.43MeV).
The atomic mass of 12N is 12.018613 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?
A radioactive isotope is being produced at a constant rate dN/dt = R in an experiment. The isotope has a half-life t1/2. Show that after a time t >> t1/2 the number of active nuclei will become constant. Find the value of this constant.
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.
Obtain a relation between the half-life of a radioactive substance and decay constant (λ).
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.
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.
Disintegration rate of a sample is 1010 per hour at 20 hours from the start. It reduces to 6.3 x 109 per hour after 30 hours. Calculate its half-life and the initial number of radioactive atoms in the sample.
Obtain an expression for the decay law of radioactivity. Hence show that the activity A(t) =λNO e-λt.
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 ______.
What percentage of radioactive substance is left after five half-lives?
Two electrons are ejected in opposite directions from radioactive atoms in a sample of radioactive material. Let c denote the speed of light. Each electron has a speed of 0.67 c as measured by an observer in the laboratory. Their relative velocity is given by ______.
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 :
Suppose we consider a large number of containers each containing initially 10000 atoms of a radioactive material with a half life of 1 year. After 1 year ______.
When a nucleus in an atom undergoes a radioactive decay, the electronic energy levels of the atom ______.
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?
Two radioactive materials A and B have decay constants \[6\lambda\] and \[2\lambda\] respectively. If initially they have same number of nuclei, then the ratio of the number of nuclei of A to that of B will be \[\frac{1}{\mathrm{e}}\] after time ______.
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 ______.
