Law of Radioactive Decay

Using the equation `N = N_0e^(-lambdat)` obtain the relation between half-life (T) and decay constant (`lambda`) of a radioactive substance.

When charcoal is prepared from a living tree, it shows a disintegration rate of 15.3 disintegrations of ¹⁴C per gram per minute. A sample from an ancient piece of charcoal shows ¹⁴C activity to be 12.3 disintegrations per gram per minute. How old is this sample? Half-life of ¹⁴C is 5730 y.

(a) Derive the relation between the decay constant and half life of a radioactive substance. 
(b) A radioactive element reduces to 25% of its initial mass in 1000 years. Find its half life.

The decay constant of ²³⁸U is 4.9 × 10⁻¹⁸ S⁻¹. (a) What is the average-life of ²³⁸U? (b) What is the half-life of ²³⁸U? (c) By what factor does the activity of a ²³⁸U sample decrease in 9 × 10⁹ years?

Lithium (Z = 3) has two stable isotopes ⁶Li and ⁷Li. When neutrons are bombarded on lithium sample, electrons and α-particles are ejected. Write down the nuclear process taking place.

Obtain an expression for the decay law of radioactivity. Hence show that the activity A(t) =λN_O e^-λt.  

Represent Radioactive Decay curve using relation `N = N_o e^(-lambdat)` graphically

A radioactive nucleus ‘A’ undergoes a series of decays according to the following scheme:

The mass number and atomic number of A are 180 and 72 respectively. What are these numbers for A₄?