Advertisements
Advertisements
प्रश्न
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.
उत्तर
Given:-
Volume of the vessel, V = 125 cm3 = 0.125 L
Half-life time of tritium, t1/2 = 12.3 y = 3.82 × 108 s
Pressure, P = 500 kpa = 5 atm
Temperature, T = 300 K,
Disintegration constant, `lambda = 0.693/t_"1/2"`
`0.693/(3.82 xx 10^8) = 0.1814 xx 10^-8`
`= 1.81 xx 10^-9 "s"^-1`
No. of atoms left undecayed, N = n × 6.023 × 1023
`= (5 xx 0.125)/(8.2 xx 10^-2 xx 3 xx 10^2) xx 6.023 xx 10^23...............(because n = "PV"/"RT")`
`= 1.5 xx 10^22` atoms
Activity, A = λN
`= 1.81 xx 10^-9 xx 1.5 xx 10^22 = 2.7 xx 10^13 " disintegration/sec"`
`therefore A = (2.7 xx 10^13)/(3.7 xx 10^10) "Ci" = 729.72` `"Ci"`
APPEARS IN
संबंधित प्रश्न
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?
Write nuclear reaction equation for α-decay of `""_88^226"Ra"`.
Write nuclear reaction equation for β−-decay of `""_15^32"P"`.
Write nuclear reaction equation for β−-decay of `""_83^210"Bi"`.
Write nuclear reaction equation for β+-decay of `""_43^97"Tc"`.
Write nuclear reaction equation for electron capture of `""_54^120"Xe"`.
Define ‘activity’ of a radioactive material and write its S.I. units.
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.
A certain sample of a radioactive material decays at the rate of 500 per second at a certain time. The count rate falls to 200 per second after 50 minutes. (a) What is the decay constant of the sample? (b) What is its half-life?
The half-life of 226Ra is 1602 y. Calculate the activity of 0.1 g of RaCl2 in which all the radium is in the form of 226Ra. Taken atomic weight of Ra to be 226 g mol−1 and that of Cl to be 35.5 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?
`""_80^197`Hg decay to `""_79^197`Au through electron capture with a decay constant of 0.257 per day. (a) What other particle or particles are emitted in the decay? (b) Assume that the electron is captured from the K shell. Use Moseley's law √v = a(Z − b) with a = 4.95 × 107s−1/2 and b = 1 to find the wavelength of the Kα X-ray emitted following the electron capture.
Radioactive isotopes are produced in a nuclear physics experiment at a constant rate dN/dt = R. An inductor of inductance 100 mH, a resistor of resistance 100 Ω and a battery are connected to form a series circuit. The circuit is switched on at the instant the production of radioactive isotope starts. It is found that i/N remains constant in time where i is the current in the circuit at time t and N is the number of active nuclei at time t. Find the half-life of the isotope.
In a gamma ray emission from nucleus :
Plot a graph showing the variation of undecayed nuclei N versus time t. From the graph, find out how one can determine the half-life and average life of the radioactive nuclei.
The half-life of a certain radioactive element is 3.465 days. Find its disintegration constant.
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 ______.
