Advertisements
Advertisements
प्रश्न
Show that half life period of radioactive material varies inversely to decay constant λ.
Advertisements
उत्तर
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`
संबंधित प्रश्न
What is gamma decay?
Describe alpha decay and write down the formula for the energy generated in this decay.
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.
Derive the relationship between half-life and decay constant of a radioelement.
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?
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 half-life of a certain radioactive species is 6.93 × 105 seconds. What is the decay constant?
The half-life of a certain radioactive nucleus is 3.2 days. Calculate (i) decay constant (ii) average life of radioactive nucleus.
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 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]
Most excited states of an atom have life times of about ____________.
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 ______.
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.
Show that the number of nuclei of a radioactive material decreases exponentially with time.
In one mean lifetime of a radioactive element the fraction of the nuclei that has disintegrated is ______. [e is the base of natural logarithm]
