Radioactivity - Introduction of Radioactivity

`""_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 K_α X-ray emitted following the electron capture.

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(t_1/2 = 14.3 days) source if it was originally purchased for 800 rupees?

A human body excretes (removes by waste discharge, sweating, etc.) certain materials by a law similar to radioactivity. If technetium is injected in some form in a human body, the body excretes half the amount in 24 hours. A patient is given an injection containing ⁹⁹Tc. This isotope is radioactive with a half-life of 6 hours. The activity from the body just after the injection is 6 μCi. How much time will elapse before the activity falls to 3 μCi?

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?

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.

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?

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? 

Write nuclear reaction equation for β⁺-decay of `""_6^11"C"`.