Advertisements
Advertisements
प्रश्न
The half-life for radioactive decay of 14C is 5730 years. An archaeological artifact containing wood had only 80% of the 14C found in a living tree. Estimate the age of the sample.
Advertisements
उत्तर
Radioactive decay follows first-order kinetics.
∴ Decay constant (λ) = `0.693/t_(1//2)`
= `0.693/5730` year−1
[R]0 = 100 ...[Given]
∴ [R] = 80
t = `2.303/λ log [R]_0/[R]`
= `2.303/((0.693/5730)) log 100/80`
= `(2.303 xx 5730)/0.693 xx 0.0969` year
= 1845 years
Hence, the age of the sample is 1845 years.
संबंधित प्रश्न
Sucrose decomposes in acid solution to give glucose and fructose according to the first order rate law. The half life of the reaction is 3 hours. Calculate fraction of sucrose which will remain after 8 hours.
For a first order reaction, show that time required for 99% completion is twice the time required for the completion of 90% of reaction.
A first order reaction takes 40 minutes for 30% decomposition. Calculate t1/2 for this reaction. (Given log 1.428 = 0.1548)
A first order reaction takes 23.1 minutes for 50% completion. Calculate the time required for 75% completion of this reaction.
(log 2 = 0.301, log 3 = 0.4771, log 4 = 0.6021)
Calculate the half-life of a first order reaction from the rate constant given below:
200 s−1
The experimental data for decomposition of N2O5
\[\ce{2N2O5 -> 4NO2 + O2}\]
in gas phase at 318 K are given below:
| t/s | 0 | 400 | 800 | 1200 | 1600 | 2000 | 2400 | 2800 | 3200 |
| 102 × [N2O5]/mol L−1 | 1.63 | 1.36 | 1.14 | 0.93 | 0.78 | 0.64 | 0.53 | 0.43 | 0.35 |
- Plot [N2O5] against t.
- Find the half-life period for the reaction.
- Draw a graph between log [N2O5] and t.
- What is the rate law?
- Calculate the rate constant.
- Calculate the half-life period from k and compare it with (ii).
During nuclear explosion, one of the products is 90Sr with half-life of 28.1 years. If 1μg of 90Sr was absorbed in the bones of a newly born baby instead of calcium, how much of it will remain after 10 years and 60 years if it is not lost metabolically?
The unit of rate constant for zero order reaction is _______.
(A) t–1
(B) mol dm–3 t–1
(C) mol–1 dm3 t–1
(D) mol–2 dm6 t–1
The half life period of a first order reaction is 6. 0 h . Calculate the rate constant
The half life period of a radioactive element is 140 days. After 560 days, 1 g of element will be reduced to
Show that for a first order reaction half life is independent of initial concentration.
The rate constant for a first order reaction is 1.54 × 10−3 s−1. Calculate its half life time.
A first-order reaction takes 69.3 min for 50% completion. What is the time needed for 80% of the reaction to get completed? (Given: log 5 = 0.6990, log 8 = 0.9030, log 2 = 0.3010)
A sample of U238 (half-life = 4.5 × 109 years) ore is found to contain 23.8 g of U238 and 20.6 g of Pb206. The age of the ore is ______ × 109 years.
The amount of C-14 isotope in a piece of wood is found to be 1/16th of its amount present in a fresh piece of wood. The age of wood, half-life period of C-14 is 5770 years, is ______ years.
A reaction has a half-life of 1 min. The time required for 99.9% completion of the reaction is ______ min.
(Round off to the nearest integer).
[Use: In 2 = 0.69; In 10 = 2.3]
Assertion (A): The half-life of a reaction is the time in which the concentration of the reactant is reduced to one-half of its initial concentration.
Reason (R): In first-order kinetics, when the concentration of reactant is doubled, its half-life is doubled.
Calculate the half-life of a first order reaction from the rate constant given below:
2 min−1
