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?
Complete the following equation describing nuclear decay.
\[\ce{_7^12N -> _6^12C {+}}\] ______
Write relation between decay constant of a radioelement and its half-life.
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?
0.5 g sample of 201Tl decays to 0.0788 g in 8 days. What is its half-life?
65% of 111In sample decays in 4.2 d. What is its half-life?
A 3/4 of the original amount of radioisotope decays in 60 minutes. What is its half-life?
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)
In Hydrogen, the electron jumps from the fourth orbit to the second orbit. The wavenumber of the radiations emitted by an electron is ______
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?
Show that for radioactive decay N(t) = `"N"_"O" "e"^{-λ"t"}`, where symbols have their usual meaning.
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]
A radioactive substance has half life of 3 hours. 75 % of the substance would decay in ____________.
What is alpha decay?
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)
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 ______.
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?
In one mean lifetime of a radioactive element the fraction of the nuclei that has disintegrated is ______. [e is the base of natural logarithm]
