Advertisements
Advertisements
प्रश्न
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.
उत्तर
The strength of the radioactive source is given as:
`"dN"/"dt"` = 8.0 mCi
= 8 × 10−3 × 3.7 × 1010
= 29.6 × 10−7 decay/s
N = Required number of atoms
Half-life of `""_27^60"Co"`, `"T"_(1/2)` = 5.3 years
= 5.3 × 365 × 24 × 60 × 60
= 1.67 × 108 s
For decay constant λ, we have the rate of decay as:
`"dN"/"dt" = lambda"N"`
Where, `lambda = 0.693/"T"_(1/2) = 0.693/(1.67 xx 10^8) "s"^(-1)`
∴ N = `1/lambda ("dN")/"dt"`
= `(29.6 xx 10^7)/(0.639/(1.67 xx 10^8))`
= 7.133 × 1016 atom
For `""_27^60"Co"`
Mass of 6.023 × 1023 (Avogadro’s number) atoms = 60 g
∴ Mass of 7.133 × 1016 atom
= `(60 xx 7.133 xx 10^16)/(6.023 xx 10^23)`
= 7.106 × 10−6 g
Hence, the amount of For `""_27^60"Co"` necessary for the purpose is 7.106 × 10−6 g.
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.
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?
The half-life of `""_38^90 "Sr"` is 28 years. What is the disintegration rate of 15 mg of this isotope?
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 'activity' of a radioactive substance ?
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.
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 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?
The half-life of 40K is 1.30 × 109 y. A sample of 1.00 g of pure KCI gives 160 counts s−1. Calculate the relative abundance of 40K (fraction of 40K present) in natural potassium.
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 ______.
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 half-life of `""_82^210Pb` is 22.3 y. How long will it take for its activity 0 30% of the initial activity?
