Advertisements
Advertisements
प्रश्न
Show that for radioactive decay N(t) = `"N"_"O" "e"^{-λ"t"}`, where symbols have their usual meaning.
Advertisements
उत्तर
If ‘N(t)’ is the number of parent nuclei present at any instant ‘t’, ‘dN’ is the number of nuclei disintegrated in the short interval of time ‘dt’, then,
dN ∝ −N(t) dt
dN = −λ N(t) dt
where λ is known as decay constant or disintegration constant.
The negative sign indicates the disintegration of atoms.
Integrating both sides of the equation,
`int_{"N"_0}^{"N"("t")} "dN"/("N"("t")) = int_0^"t" -lambda "dt"`
where N0 is a number of parent atoms at time t = 0.
∴ loge `("N"("t"))/"N"_0 = -lambda"t"`
∴ N(t) = N0 `"e"^{-lambda"t"}`
This is the required relation.
संबंधित प्रश्न
Describe alpha, beta and gamma decays and write down the formulae for the energies generated in each of these decays.
Complete the following equation describing nuclear decay.
\[\ce{_88^226Ra->_2^4\alpha {+}}\] ______.
Complete the following equation describing nuclear decay.
\[\ce{_7^12N -> _6^12C {+}}\] ______
Choose the correct option.
\[\ce{^60_27CO}\] decays with a half-life of 5.27 years to produce \[\ce{^60_28Ni}\]. What is the decay constant for such radioactive disintegration?
Decay constant of 197Hg is 0.017 h-1. What is its half-life?
The half-life of 18F is 110 minutes. What fraction of 18F sample decays in 20 minutes?
The half-life of 35S is 87.8 d. What percentage of 35S sample remains after 180 d?
The half-life of 67Ga is 78 h. How long will it take to decay 12% of the sample of Ga?
0.5 g sample of 201Tl decays to 0.0788 g in 8 days. What is its half-life?
65% of 111In sample decays in 4.2 d. What is its half-life?
A sample of 32P initially shows activity of one Curie. After 303 days, the activity falls to 1.5 × 104 dps. What is the half-life of 32P?
The half-life of a certain radioactive species is 6.93 × 105 seconds. What is the decay constant?
Show that half life period of radioactive material varies inversely to decay constant λ.
Obtain an expression for the half-lifetime of radioactive material. Hence state the relation between an average life and half life time of radioactive material.
A radioactive substance decays to (1/10)th of its original value in 56 days. Calculate its decay constant.
A radioactive nucleus emits 4 α-particles and 7 β-particles in succession. The ratio of number of neutrons of that of protons, is
[A = mass number, Z =atomic number]
The rate of radioactive disintegration at an instant for a radioactive sample of half-life 2.2 x 109 s is 1010 s-1. The number of radioactive atoms in that sample at that instant is, ______
The activity of a radioactive sample ____________.
The radioactivity of a sample is R1 at a time T1 and R2 at a time T2. If the half-life of the specimen is T, the number of atoms that have disintegrated in the time (T1 - T2) is proportional to ______.
The activity of a radioactive substance decreases by a factor of 32 in one hour. The half-life of the substance (in min) is ______.
A radioactive sample S1 having the activity A1 has twice the number of nuclei as another sample S2 of activity A2 If A2 = 2A1 then the ratio of half-life of S1 to the half-life of S2 is ______.
The graph obtained by plotting loge (A) [A is the activity of a radioactive sample] against t (time) out of the following is:
If the number of nuclei of a radioactive substance becomes `1/e` times the initial number in 10 days, what is the decay constant of the substance?
