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
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.
\[\ce{_90^228Th->\alpha { +}}\] _____
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?
The half-life of 18F is 110 minutes. What fraction of 18F sample decays in 20 minutes?
The half-life of 35S is 87.8 d. What percentage of 35S sample remains after 180 d?
The half-life of 67Ga is 78 h. How long will it take to decay 12% of the sample of Ga?
65% of 111In sample decays in 4.2 d. 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 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 substance decays to (1/10)th of its original value in 56 days. Calculate its decay constant.
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 ____________.
The activity of a radioactive sample ____________.
What is alpha decay?
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 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.
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]
