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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

 

(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.

 

The half-life of `""_38^90 "Sr"` is 28 years. What is the disintegration rate of 15 mg of this isotope?


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.


Using the equation `N = N_0e^(-lambdat)` obtain the relation between half-life (T) and decay constant (`lambda`) of a radioactive substance.


Define 'activity' of a radioactive substance ?


Two different radioactive elements with half lives T1 and T2 have N1 and N2 undecayed atoms respectively present at a given instant. Derive an expression for the ratio of their activities at this instant in terms of N1 and N2 ?


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 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.)


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?


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.


Define one Becquerel.


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 ______


What percentage of radioactive substance is left after five half-lives?


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?

  1. Decay constant of A is greater than that of B, hence A always decays faster than B.
  2. Decay constant of B is greater than that of A but its decay rate is always smaller than that of A.
  3. Decay constant of A is greater than that of B but it does not always decay faster than B.
  4. 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.

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?


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