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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+- - Physics

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प्रश्न

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?

योग
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उत्तर

According to the question, when the β+ decays to half of its original amount, the emission rate of γ-rays will drop to half. For this, the sample will take 270 days.

Therefore, the required time is 270 days.

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अध्याय 24: The Nucleus - Exercises [पृष्ठ ४४३]

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एचसी वर्मा Concepts of Physics Vol. 2 [English] Class 11 and 12
अध्याय 24 The Nucleus
Exercises | Q 28 | पृष्ठ ४४३

संबंधित प्रश्न

State the law of radioactive decay.


Obtain the relation between the decay constant and half life of a radioactive sample.


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 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?


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.


(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.


Why is it experimentally found difficult to detect neutrinos in this process ?


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.


In a radioactive decay, neither the atomic number nor the mass number changes. Which of the following particles is emitted in the decay?


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.


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?


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.


Which one of the following nuclei has shorter meant life?

 


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 ______.


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.

The activity R of an unknown radioactive nuclide is measured at hourly intervals. The results found are tabulated as follows:

t (h) 0 1 2 3 4
R (MBq) 100 35.36 12.51 4.42 1.56
  1. Plot the graph of R versus t and calculate the half-life from the graph.
  2. Plot the graph of ln `(R/R_0)` versus t and obtain the value of half-life from the graph.

The half-life of `""_82^210Pb` is 22.3 y. How long will it take for its activity 0 30% of the initial activity?


For the following reaction, the particle 'x' is 6C115B11 + β + X ______.


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