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
What is gamma decay?
Sample of carbon obtained from any living organism has a decay rate of 15.3 decays per gram per minute. A sample of carbon obtained from very old charcoal shows a disintegration rate of 12.3 disintegrations per gram per minute. Determine the age of the old sample given the decay constant of carbon to be 3.839 × 10−12per second.
Complete the following equation describing nuclear decay.
\[\ce{_7^12N -> _6^12C {+}}\] ______
Write relation between decay constant of a radioelement and its half-life.
The half-life of 35S is 87.8 d. What percentage of 35S sample remains after 180 d?
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 3/4 of the original amount of radioisotope decays in 60 minutes. 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 radon is 3.82 d. By what time would 99.9% of radon will be decayed?
In Hydrogen, the electron jumps from the fourth orbit to the second orbit. The wavenumber of the radiations emitted by an electron is ______
The decay constant λ of a certain radioactive material is 0.2166 per day. The average life τ of the radioactive material is ______
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 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]
A radioactive substance of half-life 69.3 days is kept in a container. The time in which 80% of the substance will disintegrate will be ______
[take ln(5) = 1.61]
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, ______
Most excited states of an atom have life times of about ____________.
The activity of a radioactive sample ____________.
What is alpha decay?
A radioactive element has rate of disintegration 10,000 disintegrations per minute at a particular instant. After four minutes it become 2500 disintegrations per minute. The decay constant per minute is ______.
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:
Define half-life period.
