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
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 decay and write down the formula for the energy generated in this decay.
Complete the following equation describing nuclear decay.
\[\ce{_8^19O->e^- { +}}\] _____
Complete the following equation describing nuclear decay.
\[\ce{_90^228Th->\alpha { +}}\] _____
Decay constant of 197Hg is 0.017 h-1. What is its half-life?
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?
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?
The half-life of a certain radioactive nucleus is 3.2 days. Calculate (i) decay constant (ii) average life of radioactive nucleus.
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, ______
What is alpha 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 ______.
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 half-life of a radioactive substance is 10 days. The time taken for the `(7/8)^"th"` of the sample of disintegrates 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 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.
Show that the number of nuclei of a radioactive material decreases exponentially with time.
The half-life of \[\ce{^238_92U}\] undergoing ∝- -decay is 4.5 × 109 years. What is the activity of 1g sample of \[\ce{^238_92U}\]?
