Advertisements
Advertisements
प्रश्न
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.
Derive an expression for ‘Half Life Time’ of a radioactive material using the ‘Law of Radioactive Decay’.
Advertisements
उत्तर
Expression for half-life period (T1/2):
From the law of radioactive decay,
N = N0 e⁻λT ...(i)
where,
N → is the number of nuclei present at any instant ‘t’
N0 → is the number of parent atoms at time ‘t’ = 0
λ → is Decay constant.
Substituting N = `N_0/2` and t = T1/2 ....(where T is half life period) in equation (i),
`"N"_0/2 = "N"_0 e^(-λT)`
`1/2 = e^(-λT)`
∴ 2 = eλT
Taking log on both sides,
∴ loge 2 = λT1/2
∴ λT1/2 = loge2 = 2.303 log102
∴ λT1/2 = 2.303 × 0.3010
∴ T1/2 = `0.693/λ`
This is the required relation for the half-life in terms of the decay constant of a radioactive element.
Relation between average life (τ) and a half lifetime of radioactive material:
T1/2 = τ ln 2 = 0.693 τ
Notes
Students should refer to the answer according to the question.
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.
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.
\[\ce{_90^228Th->\alpha { +}}\] _____
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?
Derive the relationship between half-life and decay constant of a radioelement.
The half-life of 18F is 110 minutes. What fraction of 18F sample decays in 20 minutes?
0.5 g sample of 201Tl decays to 0.0788 g in 8 days. 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?
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.
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, ______
A radioactive substance has half life of 3 hours. 75 % of the substance would decay in ____________.
What is beta decay?
For radioactive substances, the fraction of its initial quantity (N0) which will disintegrate in its average lifetime is about ______.
(e = 2.71)
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:
The half-life of \[\ce{^238_92U}\] undergoing ∝- -decay is 4.5 × 109 years. What is the activity of 1g sample of \[\ce{^238_92U}\]?
