Advertisements
Advertisements
प्रश्न
The half-life of a certain radioactive nucleus is 3.2 days. Calculate (i) decay constant (ii) average life of radioactive nucleus.
Advertisements
उत्तर
Given: T1/2 = 3.2 days
To find:
- decay constant (λ)
- average life (τ)
Formulae:
- T1/2 = `0.693/lambda`
- `tau = 1/lambda`
Calculation:
From formula (i),
3.2 = `0.693/lambda`
∴ `lambda = 0.693/3.2`
∴ λ = antilog {log(0.693) − log(3.2)}
= antilog {`overline1`.8407 − 0.5051}
= antilog {`overline1`.3356}
= 0.2166 /day
From formula (ii),
`tau = 1/0.2166`
Using reciprocal table,
`tau` = 4.617 days
- The decay constant of reaction is 0.2166 /day.
- The mean life of the species is 4.617 days.
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.
\[\ce{_8^19O->e^- { +}}\] _____
Complete the following equation describing nuclear decay.
\[\ce{_7^12N -> _6^12C {+}}\] ______
Write relation between decay constant of a radioelement and its half-life.
Derive the relationship between half-life and decay constant of a radioelement.
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?
A sample of old wood shows 7.0 dps/g. If the fresh sample of tree shows 16.0 dps/g, how old is the given sample of wood? (Half-life of 14C is 5730 y)
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.
Show that for radioactive decay N(t) = `"N"_"O" "e"^{-λ"t"}`, where symbols have their usual meaning.
A radioactive substance decays to (1/10)th of its original value in 56 days. Calculate its decay constant.
The activity of a radioactive sample ____________.
What is beta decay?
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 ______.
For radioactive substances, the fraction of its initial quantity (N0) which will disintegrate in its average lifetime is about ______.
(e = 2.71)
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 half-life of \[\ce{^238_92U}\] undergoing ∝- -decay is 4.5 × 109 years. What is the activity of 1g sample of \[\ce{^238_92U}\]?
Define half-life period.
In one mean lifetime of a radioactive element the fraction of the nuclei that has disintegrated is ______. [e is the base of natural logarithm]
