Advertisements
Advertisements
Question
A radioactive substance decays to (1/10)th of its original value in 56 days. Calculate its decay constant.
Advertisements
Solution
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.
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.
\[\ce{_7^12N -> _6^12C {+}}\] ______
The half-life of 18F is 110 minutes. What fraction of 18F sample decays in 20 minutes?
The half-life of 67Ga is 78 h. How long will it take to decay 12% of the sample of Ga?
0.5 g sample of 201Tl decays to 0.0788 g in 8 days. 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?
Show that half life period of radioactive material varies inversely to decay constant λ.
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.
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, ______
Most excited states of an atom have life times of about ____________.
The activity of a radioactive sample ____________.
What is alpha decay?
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 ______.
The activity of a radioactive substance decreases by a factor of 32 in one hour. The half-life of the substance (in min) 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 ______.
Define half-life period.
