Question Based on Paragraph - Physics


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?



(a) Aarti has displayed awareness and care towards the health of her sister.

(b) During the intake of different elements and compounds, the biological organisms absorb them differently. Also, the exact distribution of the elements and their function in the various parts of organisms cannot be known clearly. For this, a radioisotope is made to enter the organism along with the elements and compounds, whose absorption, functioning and distribution to the brain has to be studied. The radioisotope acts as a tag of label for the element or compound under study. By detecting the radiation emitted by the isotope from the brain, the details regarding the absorption and function of the compounds by the organisms are found out. In this way, radioisotopes help a doctor to diagnose brain tumour.

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2013-2014 (March) All India Set 2


Write nuclear reaction equation for β-decay of `""_15^32"P"`.

Write nuclear reaction equation for electron capture of `""_54^120"Xe"`.

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.

A radioactive nucleus has a decay constant λ = 0.3465 (day)–1. How long would it take the nucleus to decay to 75% of its initial amount?

Define ‘activity’ of a radioactive material and write its S.I. units.

The sequence of stepwise decay of a radioactive nucleus is

If the atomic number and mass number of D2 are 71 and 176 respectively, what are their corresponding values of D?

State the law of radioactive decay. hence derive the relation N = Noe-λt . Represent it graphically.

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?

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 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.

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.

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.

The count rate of nuclear radiation coming from a radiation coming from a radioactive sample containing 128I varies with time as follows.

Time t (minute): 0 25 50 75 100
Ctount rate R (109 s−1): 30 16 8.0 3.8 2.0

(a) Plot In (R0/R) against t. (b) From the slope of the best straight line through the points, find the decay constant λ. (c) Calculate the half-life t1/2.

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?

In a gamma ray emission from nucleus : 

The half-life of radium is 1550 years. Calculate its disintegration constant (`lambda`) . 

Copy and complete the following table for a radioactive element whose half-life is 10 minutes. Assume that you have 30g of this element at t = 0.


A radioactive substance decays to 1/16th of its initial mass in 40 days. The half-life of the substance, in days, is: 

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.

Half life of a certain radioactive material is 8 hours.
If one starts with 600 g of this substance, how much of it will disintegrate in one day? 

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 ______.


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