The half-life of a radioactive sample undergoing α - 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 ____________. - Physics

Advertisements
Advertisements
MCQ
Fill in the Blanks

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 ____________.

Options

  • 103 Bq

  • 104 Bq

  • 105 Bq

  • 106 Bq

Advertisements

Solution

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 104 Bq.

Explanation:

Activity of the sample is given by,

`abs "R" = lambda "N"`

`abs "R" = 0.693/"T" xx "N"`

`abs "R" = 0.693/(1.4 xx 10^17) xx 2 xx 10^21`

`abs "R" = 9900 approx 10000`

` = 10^4  "Bq"`

  Is there an error in this question or solution?

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.

 

State the law of radioactive decay.


Derive the mathematical expression for law of radioactive decay for a sample of a radioactive nucleus


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.


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.


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.


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?


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.)


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?


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?


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.


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.


Obtain a relation between the half-life of a radioactive substance and decay constant (λ).


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?


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?


A source contains two species of phosphorous nuclei, \[\ce{_15^32P}\] (T1/2 = 14.3 d) and \[\ce{_15^33P}\] (T1/2 = 25.3 d). At time t = 0, 90% of the decays are from \[\ce{_15^32P}\]. How much time has to elapse for only 15% of the decays to be from \[\ce{_15^32P}\]?


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 ______.


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 :


The half-life of the radioactive substance is 40 days. The substance will disintegrate completely in


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?

  1. Initial rate of decay of A is twice the initial rate of decay of B and λA = λB.
  2. Initial rate of decay of A is twice the initial rate of decay of B and λA > λB.
  3. Initial rate of decay of B is twice the initial rate of decay of A and λA > λB.
  4. Initial rate of decay of B is the same as the rate of decay of A at t = 2h and λB < λA.

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.


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?


Share
Notifications



      Forgot password?
Use app×