Advertisements
Advertisements
Question
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.
Advertisements
Solution
Data: 15.3 decays per gram per minute (living organism), 12.3 disintegrations per gram per minute (very old charcoal). Hence, we have,
`("A"("t"))/"A"_0 = 12.3/15.3`, λ = 3.839 x 10-12 per second
A(t) = A0e-λt ∴ `"e"^(lambda"t") = "A"_0/"A"`
∴ `lambda"t" = log_"e"("A"_0/"A")`
∴ t = `2.303/lambda log_10 ("A"_0/"A")`
`= 2.303/(3.839 xx 10^-12)log_10(15.3/12.3)`
`= (2.303 xx 10^12)/3.839`(log 15.3 - log 12.3)
`= (2.303 xx 10^12)/3.839 (1.1847 - 1.0899)`
`= ((2.303)(0.0948))/3.839 xx 10^12`s
= 5.687 x 1010 s
`= (5.687 xx 10^10 "s")/(3.156 xx 10^7 "s per year")`
= 1802 years
APPEARS IN
RELATED QUESTIONS
Complete the following equation describing nuclear decay.
\[\ce{_88^226Ra->_2^4\alpha {+}}\] ______.
Complete the following equation describing nuclear decay.
\[\ce{_8^19O->e^- { +}}\] _____
Complete the following equation describing nuclear decay.
\[\ce{_90^228Th->\alpha { +}}\] _____
Complete the following equation describing nuclear decay.
\[\ce{_7^12N -> _6^12C {+}}\] ______
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?
Write relation between decay constant of a radioelement and its half-life.
Derive the relationship between half-life and decay constant of a radioelement.
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?
The half-life of radon is 3.82 d. By what time would 99.9% of radon will be decayed?
In Hydrogen, the electron jumps from the fourth orbit to the second orbit. The wavenumber of the radiations emitted by an electron is ______
The half-life of a certain radioactive species is 6.93 × 105 seconds. What is the decay constant?
Show that half life period of radioactive material varies inversely to decay constant λ.
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]
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]
What is alpha 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 ______.
For radioactive substances, the fraction of its initial quantity (N0) which will disintegrate in its average lifetime is about ______.
(e = 2.71)
The graph obtained by plotting loge (A) [A is the activity of a radioactive sample] against t (time) out of the following is:
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.
