“Radioactive Decay Law” MHT-CET Class 12 Physics Crash Course| Chapter Structure of Atoms and Nuclei
In this session G.S. Khairnar will discuss the theory and MCQ’s of “Radioactive Decay Law”. The session will be useful for all the aspirants of MHT-CET 2022. The session will be in Marathi and English.
Radioactive Decay Law
Points to recall:
We have leant that, the phenomenon of spontaneous emission of radiations from radioactive substance is known as radioactive decay. Radioactivity is nuclear phenomenon in which an unstable nucleus undergoes decay. It is called radioactive decay.
There are three types of decay,
- α Decay in which a helium nucleus
is emitted. - β Decay in which electrons or positrons are emitted.
- γ Decay in which high energy photons are emitted.
is emitted.Let’s study the law of radioactive decay…….!
The spontaneous breaking of nucleus is known as radioactive disintegration.
The Decay Law: – The number of nuclei undergoing the decay per unit time is proportional to the number of unchanged nuclei present at that instant.
Let N be the number of nuclei present at any instant t, dN be the number of nuclei that disintegrated in short interval of time dt. Then according to decay law,
Where λ is known as decay constant or disintegration constant.
From eq (1)
Integrating both sides
Where c is constant of integration whose value depends on initial conditions.
At, t = 0 ; N = N₀ (the number of original nuclei)
So, logₑ N₀ = 0 + c ———-(3)
Substituting the value in above expression
This expression shows that number of nuclei of given radioactive substance decreases exponentially with time.
Decay Constant: –
The decay constant is defined as ratio of the amount of substance disintegrated per unit time to amount of substance present at that time.
Half life Period (T): –
Half life period (T) of radioactive substance is defined as the time in which the half substance is disintegrated.
Radioactive Decay Law
Let’s solve the following multiple choice questions………..!
Q.1) During radioactive decay in time interval of ‘t’ the substance is decayed by…..of its original quantity.
a) 27%
b) 37%
c) 47%
d) 57%
Answer
b) 37%
Q.2) Half life time of radioactive substance is given as,
Q.3) Number of nuclei of given radioactive substance decreases…………
a) Linearly with time
b) Non linearly with time
c) Exponentially with time
d) None of these.
Answer
d) They are neutral hence not deflected by electric and magnetic field.
Q.4) The number of nuclei undergoing the decay per unit time is………..
a) Inversely proportional to the number of unchanged nuclei present at that instant.
b) Inversely proportional to the number of changed nuclei present at that instant.
c) Directly proportional to the number of unchanged nuclei present at that instant.
d) Directly proportional to the number of changed nuclei present at that instant.
Answer
c) Directly proportional to the number of unchanged nuclei present at that instant.
Q.5) If the decay or disintegration constant of a radioactive substance is, then its half life and mean life are respectively……………..
Q.6) The radioactivity of a certain radioactive element drops to 1/16 of its initial value in 16 seconds. Its half life is
(a) 2 seconds
(b) 4 seconds
(c) 5 seconds
(d) 6 seconds
Answer
(b) 4 seconds.
Q.7) If T is the half life of a radioactive material, then the fraction that will remain after a time T/2 is…..
Q.8) Decay constant of a radioactive material is 0.02 per second, then its half life time is…
a) 0.3465 sec
b) 3.465 sec
c) 34.65 sec
d) 346.5 sec
Answer
c) 34.65 sec
Others MHT- CET Crash Course From Chapter “Structure of atoms and Nuclei”-
1) Bohr’s Postulates – Click Here
2) Energy of Bohr’s orbit – Click Here
3) Radius of Bohr’s orbit – Click Here
4) Hydrogen Spectrum – Click Here
5) Radioactive Decay – Click Here
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