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. - Physics (JEE Main)

Advertisements
Advertisements
MCQ
Fill in the Blanks

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.

Options

  • 60.00

  • 65.00

  • 68.00

  • 70.00

Advertisements

Solution

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 the sample is 68.00 years.

Explanation:

`N_1 = N_0e^{-lambda.10}`

`N_2 = N_0e^{-lambdax}`

`N_2/N_1 = 4/100 = e^{lambda(10 - x)}`

`e^{lambda(x - 10)} = 100/4`

λ(x - 10) = 2 ln 10 - ln 4

λ(x - 10) = 2(2.3) - 2(0.693)

λ(x - 10) = 3.22

Now, `lambda = 0.693/12.5` yr-1

∴ x - 10 = `12.5/0.693 xx 3.22`

= 58.08

x ≅ 68 years

  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.

 


State the law of radioactive decay.


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


Write symbolically the process expressing the β+ decay of `""_11^22Na`. Also write the basic nuclear process underlying this decay.


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.


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 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?


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.


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.


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).


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`


Define one Bacquerel.


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 ______.


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 :


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


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 ______.


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.


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×