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.
\[\ce{_8^19O->e^- { +}}\] _____
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?
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?
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?
In Hydrogen, the electron jumps from the fourth orbit to the second orbit. The wavenumber of the radiations emitted by an electron is ______
Show that half life period of radioactive material varies inversely to decay constant λ.
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]
Most excited states of an atom have life times of about ____________.
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 ______.
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 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.
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?
Show that the number of nuclei of a radioactive material decreases exponentially with time.
Define half-life period.
