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
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.
\[\ce{_8^19O->e^- { +}}\] _____
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?
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?
A 3/4 of the original amount of radioisotope decays in 60 minutes. What is its half-life?
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)
Show that for radioactive decay N(t) = `"N"_"O" "e"^{-λ"t"}`, where symbols have their usual meaning.
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 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 ______.
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 ______.
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 disintegration rate of a radio-active sample is 1010 per hour at 20 hours from the start. It reduces to 5 × 109 per hour after 30 hours. Calculate the decay constant.
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?
Show that the number of nuclei of a radioactive material decreases exponentially with time.
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]
