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
Complete the following equation describing nuclear decay.
\[\ce{_88^226Ra->_2^4\alpha {+}}\] ______.
Complete the following equation describing nuclear decay.
\[\ce{_90^228Th->\alpha { +}}\] _____
Complete the following equation describing nuclear decay.
\[\ce{_7^12N -> _6^12C {+}}\] ______
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?
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 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 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 species is 6.93 × 105 seconds. What is the 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]
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, ______
A radioactive substance has half life of 3 hours. 75 % of the substance would decay in ____________.
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)
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.
The half-life of \[\ce{^238_92U}\] undergoing ∝- -decay is 4.5 × 109 years. What is the activity of 1g sample of \[\ce{^238_92U}\]?
In one mean lifetime of a radioactive element the fraction of the nuclei that has disintegrated is ______. [e is the base of natural logarithm]
