Advertisements
Advertisements
प्रश्न
What is the amount of \[\ce{_27^60Co}\] necessary to provide a radioactive source of strength 10.0 mCi, its half-life being 5.3 years?
Advertisements
उत्तर
Data: Activity= 10.0 mCi = 10.0 x 10-3 Ci = (10.0 x 10-3)(3.7 x 1010) dis/s = 3.7 x 108 dis/s
T1/2 = 5.3 years = (5.3)(3.156 × 107)s = 1.673 × 108 s
Decay constant, `lambda = 0.693/("T"_(1//2)) = 0.693/(1.673 xx 10^8) "s"^-1`
= 4.142 x 10-9 s-1
∴ N = `"activity"/lambda = (3.7 xx 10^8)/(4.142 xx 10^-9)` atoms
= 8.933 × 1016 atoms
= 60 grams of \[\ce{_27^60Co}\] contain 6.02 x 1023 atoms
∴ Mass of 8.933 x 1016 atoms of \[\ce{_27^60Co}\]
`= (8.933 xx 10^16)/(6.02 xx 10^23) xx 60 "g"`
= 8.903 x 10-6 g = 8.903 µg
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.
Derive the mathematical expression for law of radioactive decay for a sample of a radioactive nucleus
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?
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 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.
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.
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.
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?
The decay constant of a radioactive sample is λ. The half-life and the average-life of the sample are respectively
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.)
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.)
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?
When charcoal is prepared from a living tree, it shows a disintegration rate of 15.3 disintegrations of 14C per gram per minute. A sample from an ancient piece of charcoal shows 14C activity to be 12.3 disintegrations per gram per minute. How old is this sample? Half-life of 14C is 5730 y.
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.
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.
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`
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.
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.
Which one of the following nuclei has shorter meant life?
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?
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 ______.
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 ______.
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 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.
Consider a radioactive nucleus A which decays to a stable nucleus C through the following sequence:
A→B→C
Here B is an intermediate nuclei which is also radioactive. Considering that there are N0 atoms of A initially, plot the graph showing the variation of number of atoms of A and B versus time.
Sometimes a radioactive nucleus decays into a nucleus which itself is radioactive. An example is :
\[\ce{^38Sulphur ->[half-life][= 2.48h] ^{38}Cl ->[half-life][= 0.62h] ^38Air (stable)}\]
Assume that we start with 1000 38S nuclei at time t = 0. The number of 38Cl is of count zero at t = 0 and will again be zero at t = ∞ . At what value of t, would the number of counts be a maximum?
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.
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?
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 ______.
