Solved problem in nuclear physics

1.        2 gram of charcoal from tree gives a radioactive carbon count of 18 disintegrations per minutes. Charcoal from museum   of 14gm of mass gives a count of 12 min^-1 .if the T_1/2 of ¹⁴C  is 5739 what is the age of the archeological specimen. Deduce the equation which produces the radioactive carbon mentioning the source of the nuclides.

2.       The ration of radiocarbon in a piece of wood 13% that of the atmosphere, calculate the age of the wood. if the disintegration constant H is 1.24 X 10^-4/year.

3.       5gm of radioactive element decays by beta emission to 0.250g  in 400hrs , calculate the decay constant.

4.       ¹³¹I has a half life period of 8 days . what is  its decay constant.

5.       If the decay constant of a radioactive element of mass 20gm is 1.234X10⁴/hrs, calculate how long the element will stay if its half life is 30 minutes.

6.       0.8g of Co decay by beta emission to 0.125g in 720,000 secs, what is its half life period

7.       What is the mean life time of a radioactive element whose half life is 60 years.

8.       The half life of ²³⁶Ra is 1620 years, calculate the half life in per sec.

9.       By natural radioactivity,²³⁸U, emits an alpha particles. the residue heavy nucleus from this radioactive process is UXI, the UX1 in turn emits beta-particles. the heavy residual nucleus from this radioactive process is called UX2, determine the atomic number of (i)UX1 (ii)UX2.

10.    At a certain instant , a radioactive materials contains 10¹² atoms . the half life of the material is 30 days.

·         calculate the number of disintegrations in the first second.

·         how long will elapse before 10⁴ atoms remain?

·         what is the count rate at this time.