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प्रश्न
State the law of radioactive decay.
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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.
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संबंधित प्रश्न
(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.
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Obtain the relation between the decay constant and half life of a radioactive sample.
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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.
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.
\[\ce{^1_1H + ^3_1H -> ^2_1H + ^2_1H}\]
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\[\ce{^223_88 Ra -> ^219_86 Rn + ^4_2He}\]
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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.
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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?
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
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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.)
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Define one Becquerel.
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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?
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\[\ce{^38Sulphur ->[half-life][= 2.48h] ^{38}Cl ->[half-life][= 0.62h] ^38Air (stable)}\]
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