Advertisements
Advertisements
Question
State the law of radioactive decay.
Advertisements
Solution
Law of radioactive decay:
The number of nuclei undergoing the decay per unit time is proportional to the number of unchanged nuclei present at that instant.
If ‘N’ is the number of nuclei present at any instant ‘t’, ‘dN’ is the number of nuclei that disintegrated in short interval of time ‘dt’, then according to decay law,
`- (dN)/dt ∝ N`
`:.(dN)/dt = -lambda N`
where, `lambda` is known as decay constant or disintegration constant. The negative sign indicates disintegration of atoms.
APPEARS IN
RELATED QUESTIONS
The decay constant of radioactive substance is 4.33 x 10-4 per year. Calculate its half life period.
(a) Write the basic nuclear process involved in the emission of β+ in a symbolic form, by a radioactive nucleus.
(b) In the reactions given below:
(i)`""_16^11C->_y^zB+x+v`
(ii)`""_6^12C+_6^12C->_a^20 Ne + _b^c He`
Find the values of x, y, and z and a, b and c.
Derive the mathematical expression for law of radioactive decay for a sample of a radioactive nucleus
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.
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.
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 \[\ce{A + b → C + d}\] 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.
\[\ce{^1_1H + ^3_1H -> ^2_1H + ^2_1H}\]
Atomic masses are given to be
`"m"(""_1^2"H")` = 2.014102 u
`"m"(""_1^3"H")` = 3.016049 u
`"m"(""_6^12"C")` = 12.000000 u
`"m"(""_10^20"Ne")` = 19.992439 u
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
Represent Radioactive Decay curve using relation `N = N_o e^(-lambdat)` graphically
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.
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.
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?
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
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.)
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.)
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?
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`
Define one Becquerel.
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.
Before the year 1900 the activity per unit mass of atmospheric carbon due to the presence of 14C averaged about 0.255 Bq per gram of carbon.
(a) What fraction of carbon atoms were 14C?
(b) An archaeological specimen containing 500 mg of carbon, shows 174 decays in one hour. What is the age of the specimen, assuming that its activity per unit mass of carbon when the specimen died was equal to the average value of the air? The half-life of 14C is 5730 years.
Obtain an expression for the decay law of radioactivity. Hence show that the activity A(t) =λNO e-λt.
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.
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?
'Half-life' of a radioactive substance accounts for ______.
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 ______.
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 :
When a nucleus in an atom undergoes a radioactive decay, the electronic energy levels of the atom ______.
Draw a graph showing the variation of decay rate with number of active nuclei.
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 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.
The half-life of `""_82^210Pb` is 22.3 y. How long will it take for its activity 0 30% of the initial activity?
For the following reaction, the particle 'x' is 6C11 → 5B11 + β + X ______.
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 ______.
