Advertisements
Advertisements
Question
Show that half life period of radioactive material varies inversely to decay constant λ.
Advertisements
Solution
From law of radioactive decay,
`"N" = "N"_0 "e"^{-lambda"t"}`
at t = `"T"_{1"/"2}, "N" = ("N"_0)/2`
∴ `("N"_0)/2 = "N"_0 "e"^{-lambda"T"_{1"/"2}}`
∴ `1/2 = "e"^{-lambda"T"_{1"/"2}}`
∴ `"e"^{lambda"T"_{1"/"2}} = 2`
∴ `lambda"T"_{1"/"2} = log_"e"2 = 0.693`
∴ `"T"_{1"/"2} = 0.693/lambda`
⇒ `"T"_{1"/"2} ∝ 1/lambda`
RELATED QUESTIONS
What is gamma decay?
Describe alpha, beta and gamma decays and write down the formulae for the energies generated in each of these decays.
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?
Decay constant of 197Hg is 0.017 h-1. What is its half-life?
The half-life of 18F is 110 minutes. What fraction of 18F sample decays in 20 minutes?
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 half-life of radon is 3.82 d. By what time would 99.9% of radon will be decayed?
A sample of old wood shows 7.0 dps/g. If the fresh sample of tree shows 16.0 dps/g, how old is the given sample of wood? (Half-life of 14C is 5730 y)
The decay constant λ of a certain radioactive material is 0.2166 per day. The average life τ of the radioactive material is ______
The half-life of a certain radioactive species is 6.93 × 105 seconds. What is the decay constant?
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 decays to (1/10)th of its original value in 56 days. Calculate its decay constant.
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]
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 ____________.
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 ______.
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 half-life of a radioactive substance is 10 days. The time taken for the `(7/8)^"th"` of the sample of disintegrates 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]
