Advertisements
Advertisements
प्रश्न
Derive the relationship between half-life and decay constant of a radioelement.
Advertisements
उत्तर
Equation for the decay constant is given as,
`lambda = 2.303/"t" log_10 "N"_0/"N"` ....(i)
Where, λ = Decay constant
N = Number of nuclei (atoms) present at time t
At t = 0, N = N0.
Hence, at t = t1/2, N = N0/2
Substitution of these values of N and t in equation (i) gives,
`lambda = 2.303/"t"_(1//2) log_10 "N"_0/("N"_0/2)`
`= 2.303/"t"_(1//2) log_10 2 = 2.303/"t"_(1//2) xx 0.3010 = 0.693/"t"_(1//2)`
Hence, `lambda = 0.693/"t"_(1//2) or "t"_(1//2) = 0.693/lambda`
APPEARS IN
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.
\[\ce{_8^19O->e^- { +}}\] _____
Complete the following equation describing nuclear decay.
\[\ce{_90^228Th->\alpha { +}}\] _____
The half-life of 35S is 87.8 d. What percentage of 35S sample remains after 180 d?
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)
The decay constant λ of a certain radioactive material is 0.2166 per day. The average life τ of the radioactive material is ______
The half-life of a certain radioactive nucleus is 3.2 days. Calculate (i) decay constant (ii) average life of radioactive nucleus.
Show that for radioactive decay N(t) = `"N"_"O" "e"^{-λ"t"}`, where symbols have their usual meaning.
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]
Most excited states of an atom have life times of about ____________.
What is beta 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 half-life of a radioactive substance is 10 days. The time taken for the `(7/8)^"th"` of the sample of disintegrates 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?
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.
