Advertisements
Advertisements
Question
The half-life of radium is 1550 years. Calculate its disintegration constant (`lambda`) .
Solution
`T_"1/2" = 1550 "years"`
⇒ `("In" 2)/lambda = 1550 xx 365 xx 24 xx 3600 "second"`
⇒ `lambda = ("In" 2)/(1550 xx 365 xx 24 xx 3600) "s"^-1= 0.693/(1500 xx 3.1536 xx 10^7)`
⇒ `lambda = 1.418 xx 10^-11 "disintegration/second"`
APPEARS IN
RELATED QUESTIONS
The half life of a certain radioactive material against \u0003α-decay is 100 days. After how much time, will the undecayed fraction of the material be 6.25%?
For the past some time, Aarti had been observing some erratic body movement, unsteadiness and lack of coordination in the activities of her sister Radha, who also used to complain of severe headache occasionally. Aarti suggested to her parents to get a medical check-up of Radha. The doctor thoroughly examined Radha and diagnosed that she has a brain tumour.
(a) What, according to you, are the values displayed by Aarti?
(b) How can radioisotopes help a doctor to diagnose brain tumour?
Plot a graph showing variation of activity of a given radioactive sample with time.
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.
Radioactive 131I has a half-life of 8.0 days. A sample containing 131I has activity 20 µCi at t = 0. (a) What is its activity at t = 4 days? (b) What is its decay constant at t = 4.0 days?
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?
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.
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.
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`
Half-life of a certain radioactive material is 8 hours.
Find the disintegration constant of this material.
