Advertisements
Advertisements
प्रश्न
A radioactive substance decays to (1/10)th of its original value in 56 days. Calculate its decay constant.
Advertisements
उत्तर
Here, `("N"("t"))/"N" = 1/10` and t = 56 days
We have, `("N"("t"))/"N"_0 = "e"^{-lambda"t"}`
∴ `1/10 = "e"^{-lambda"t"}`
∴ `"e"^{lambda"t"} = 10`
∴ `lambda"t" = log_"e"10`
∴ `lambda = (log_"e"10)/"t"`
= `(2.303 xx log 10)/56`
= `2.303/56`
= antilog {log(2.303) − log (56)}
= antilog {0.3623 − 1.7481}
= antilog {`overline2` .6142}
= 4.113 × 10−2 per day
The decay constant is 4.113 × 10−2 per day.
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, 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.
\[\ce{_88^226Ra->_2^4\alpha {+}}\] ______.
Complete the following equation describing nuclear decay.
\[\ce{_90^228Th->\alpha { +}}\] _____
Write relation between decay constant of a radioelement and its half-life.
Decay constant of 197Hg is 0.017 h-1. What is its half-life?
The half-life of 35S is 87.8 d. What percentage of 35S sample remains after 180 d?
A 3/4 of the original amount of radioisotope decays in 60 minutes. 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 ______
Show that half life period of radioactive material varies inversely to decay constant λ.
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.
Obtain an expression for the half-lifetime of radioactive material. Hence state the relation between an average life and half life time of radioactive material.
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, ______
The activity of a radioactive sample ____________.
A radioactive substance has half life of 3 hours. 75 % of the substance would decay in ____________.
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)
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 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 \[\ce{^238_92U}\]?
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]
