Advertisements
Advertisements
प्रश्न
The half-life of a radioisotope is 10 h. Find the total number of disintegration in the tenth hour measured from a time when the activity was 1 Ci.
उत्तर
Given:
Half-life of radioisotope,`T_(1"/"2)` = 10 hrs
Initial activity, `A_0` = 1 Ci
Disintegration constant, `lambda = 0.693/(10 xx 3600) "s"^-1`
Activity of radioactive sample,
`A = A_0e^(-lambdat)`
Here, A0 = Initial activity
`lambda` = Disintegration constant
t = Time taken
After 9 hours,
Activity , `A = A_0e^(-lambdat) = 1 xx e^(-0.693/(10 xx 3600) xx 9 = 0.536` Ci
`therefore` Number of Atoms left , N = `A/lambda = (0.536 xx 10 xx 3.7 xx 10^10 xx 3600)/0.693 = 103.023 xx 10^13` After 10 hrs
Activity , A " `= A_0e^(-lambdat)`
= `1 xx e^(-0.693/10 xx 10) = 0.5` Ci
Number of atoms left after the 10th hour (`N` ")will be
A" = `lambdaN` "
N" = A"/`lambda`
= `(0.5 xx 3.7 xx 10^10 xx 3.600)/(0.693"/"10)`
= `26.37 xx 10^10 xx 3600 = 96.103 xx 10^13`
Number of disintegrations = (103.023 − 96.103) × 1013
= 6.92 × 1013
APPEARS IN
संबंधित प्रश्न
Write nuclear reaction equation for β+-decay of `""_6^11"C"`.
Draw graphs showing variation of photoelectric current with applied voltage for two incident radiations of equal frequency and different intensities. Mark the graph for the radiation of higher intensity.
The half-life of 199Au is 2.7 days. (a) Find the activity of a sample containing 1.00 µg of 198Au. (b) What will be the activity after 7 days? Take the atomic weight of 198Au to be 198 g mol−1.
The selling rate of a radioactive isotope is decided by its activity. What will be the second-hand rate of a one month old 32P(t1/2 = 14.3 days) source if it was originally purchased for 800 rupees?
A vessel of volume 125 cm3 contains tritium (3H, t1/2 = 12.3 y) at 500 kPa and 300 K. Calculate the activity of the gas.
In an agricultural experiment, a solution containing 1 mole of a radioactive material (t1/2= 14.3 days) was injected into the roots of a plant. The plant was allowed 70 hours to settle down and then activity was measured in its fruit. If the activity measured was 1 µCi, what per cent of activity is transmitted from the root to the fruit in steady state?
Natural water contains a small amount of tritium (`""_1^3H`). This isotope beta-decays with a half-life of 12.5 years. A mountaineer while climbing towards a difficult peak finds debris of some earlier unsuccessful attempt. Among other things he finds a sealed bottled of whisky. On returning, he analyses the whisky and finds that it contains only 1.5 per cent of the `""_1^3H` radioactivity as compared to a recently purchased bottle marked '8 years old'. Estimate the time of that unsuccessful attempt.
4 × 1023 tritium atoms are contained in a vessel. The half-life of decay tritium nuclei is 12.3 y. Find (a) the activity of the sample, (b) the number of decay in the next 10 hours (c) the number of decays in the next 6.15 y.
238U decays to 206Pb with a half-life of 4.47 × 109 y. This happens in a number of steps. Can you justify a single half for this chain of processes? A sample of rock is found to contain 2.00 mg of 238U and 0.600 mg of 206Pb. Assuming that all the lead has come from uranium, find the life of the rock.
A charged capacitor of capacitance C is discharged through a resistance R. A radioactive sample decays with an average-life τ. Find the value of R for which the ratio of the electrostatic field energy stored in the capacitor to the activity of the radioactive sample remains constant in time.
`""_83^212"Bi"` can disintegrate either by emitting an α-particle of by emitting a β−-particle. (a) Write the two equations showing the products of the decays. (b) The probabilities of disintegration α-and β-decays are in the ratio 7/13. The overall half-life of 212Bi is one hour. If 1 g of pure 212Bi is taken at 12.00 noon, what will be the composition of this sample at 1 P.m. the same day?
A sample contains a mixture of 108Ag and 110Ag isotopes each having an activity of 8.0 × 108 disintegration per second. 110Ag is known to have larger half-life than 108Ag. The activity A is measured as a function of time and the following data are obtained.
| Time (s) |
Activity (A) (108 disinte- grations s−1) |
Time (s) |
Activity (A 108 disinte-grations s−1) |
| 20 40 60 80 100 |
11.799 9.1680 7.4492 6.2684 5.4115 |
200 300 400 500 |
3.0828 1.8899 1.1671 0.7212 |
(a) Plot ln (A/A0) versus time. (b) See that for large values of time, the plot is nearly linear. Deduce the half-life of 110Ag from this portion of the plot. (c) Use the half-life of 110Ag to calculate the activity corresponding to 108Ag in the first 50 s. (d) Plot In (A/A0) versus time for 108Ag for the first 50 s. (e) Find the half-life of 108Ag.
In a gamma ray emission from nucleus :
The half-life of radium is 1550 years. Calculate its disintegration constant (`lambda`) .
Complete the following nuclear reactions :
(i) `"_15^32P -> ` `"_z^AX + bar(e) + bar(v)`
(ii) `"_6^12 C `+`"_6^12C ->` ` "_2^A Y + ` `"_4^2 He`
The half-life of a certain radioactive element is 3.465 days. Find its disintegration constant.
Half-life of a certain radioactive material is 8 hours.
Find the disintegration constant of this material.
A nucleus with Z = 92 emits the following in a sequence:
α, β‾, β‾, α, α, α, α, α, β‾, β‾, α, β+, β+, α
Then Z of the resulting nucleus is ______.
