Advertisements
Advertisements
Question
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.
Advertisements
Solution 1
Given:
A(t1) = 1010 per hour, where t1 = 20 h,
A(t2) = 5 × 109 per hour, where t2 = 30 h,
To find: λ = ?
Formula:
A(t) = `A_0e^{-lambdat}`
∴ `(A(t_1))/(A(t_2)) = (A_0e^{-lambdat_1})/(A_0e^{-lambdat_2}) = (e^{-lambdat_1})/(e^{-lambdat_2})`
∴ `10^10/(5 xx 10^-9) = (e^{-lambda20})/(e^{-lambda30}) = e^{lambda(30 - 20)} = e^{10lambda}`
∴ 2 = `e^{10lambda}`
∴ 2 = `e^{10lambda}`
∴ log2 = 10λloge = 10λ ..............(∵ loge = 1)
∴ 0.693 = 10λ
∴ λ = 0.0693
Solution 2
`N = N_0e^-(lambdat)`
`N_2/N_1 = e^(-lambda(t_2-t_1)`
Given:
N1 = 1.0 × 1010 per hour at t1 = 20 hours
N2 = 5.0 × 109 per hour at t2 = 30 hours
`N_2/N_1 = e^(-lambda(t_2-t_1)) =>(5xx10^9)/(1xx10^10) = e^(-lambda(10)) => 1/2 = e^(-10lambda)`
Take natural log
`(1/2) = -10lambda => -ln 2 = -10lambda => lambda = ln2/10 = 0.693/10`
= 0.0693 per hour
APPEARS IN
RELATED QUESTIONS
What is gamma decay?
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.
\[\ce{_7^12N -> _6^12C {+}}\] ______
Derive the relationship between half-life and decay constant of a radioelement.
Decay constant of 197Hg is 0.017 h-1. What is its half-life?
0.5 g sample of 201Tl decays to 0.0788 g in 8 days. What is its half-life?
A 3/4 of the original amount of radioisotope decays in 60 minutes. 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 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 ____________.
A radioactive substance has half life of 3 hours. 75 % of the substance would decay in ____________.
What is alpha decay?
The activity of a radioactive substance decreases by a factor of 32 in one hour. The half-life of the substance (in min) 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?
Show that the number of nuclei of a radioactive material decreases exponentially with time.
The half-life of \[\ce{^238_92U}\] undergoing ∝- -decay is 4.5 × 109 years. What is the activity of 1g sample of \[\ce{^238_92U}\]?
In one mean lifetime of a radioactive element the fraction of the nuclei that has disintegrated is ______. [e is the base of natural logarithm]
