Advertisements
Advertisements
प्रश्न
State the law of radioactive decay.
Advertisements
उत्तर
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
संबंधित प्रश्न
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.
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?
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 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.
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
Using the equation `N = N_0e^(-lambdat)` obtain the relation between half-life (T) and decay constant (`lambda`) of a radioactive substance.
Define 'activity' of a radioactive substance ?
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?
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.)
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?
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 one Becquerel.
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.
The isotope \[\ce{^57Co}\] decays by electron capture to \[\ce{^57Fe}\] with a half-life of 272 d. The \[\ce{^57Fe}\] nucleus is produced in an excited state, and it almost instantaneously emits gamma rays.
(a) Find the mean lifetime and decay constant for 57Co.
(b) If the activity of a radiation source 57Co is 2.0 µCi now, how many 57Co nuclei does the source contain?
c) What will be the activity after one year?
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.
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.
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 ______.
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 :
Which sample, A or B shown in figure has shorter mean-life?
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.
What is the half-life period of a radioactive material if its activity drops to 1/16th of its initial value of 30 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 ______.
