State the law of radioactive decay, Physics

State the law of radioactive decay. Show that radioactive decay is exponential in nature. Does the activity of a radioactive element depend on external physical conditions?

Law of radioactive Decay: This law states that the number of radioactive nuclei decreases exponentially with time. The rate of disintegration dN/dt, i.e., the number of atoms disintegrated per second is directly proportional to the number of atoms present (N) a that moment. This is known as Decay Law.


Let N0 be the number of atoms present in a radioactive sample initially i.e., at t = 0.

Let N be the no of atoms left at a time t and dN be the no of atoms disintegrating in a short interval of time t.

The rate of disintegration = dN/dt

According to decay law = dN/dt α N or dN/dt =  -λN

Where, λ = decay or disintegration constant. The negative sign indicates that as time

increases, the number of atoms decreases

dN/dt=  -λN OR dN/N = -λdt

Integrating the above equation

∫dN/N = -λ∫dt or logeN = -λt +c ...(1)

Where c = integration constant and it can be found in the initial condition.

i.e., If t = 0, N = N0

Then, logeN0 = c ............ (2)

From equation (1)

LogeN = - λt + logeN0

LogeN - logeN0 = -λt (or)

Loge(N/N0)= e- λt

Or N= N0e- λt


a) The number of radioactive nuclei decreases exponentially with time and reduced to zero after infinite time

b) The above equation represent radioactive decay is exponential in nature. The activity of a radioactivity element does not depend on external physical conditions like temperature, pressure etc.

Posted Date: 5/14/2013 6:20:40 AM | Location : United States

Related Discussions:- State the law of radioactive decay, Assignment Help, Ask Question on State the law of radioactive decay, Get Answer, Expert's Help, State the law of radioactive decay Discussions

Write discussion on State the law of radioactive decay
Your posts are moderated
Related Questions
Describe Kirchoffs Current Law? Ans. It defines " the current flowing toward a point in a circuit have to be equal to the current flowing away from that point. I = I 1 + I

What are polar molecules Polar molecules - molecules having of two or more atoms that are neutral but have a charge which is not distributed uniformly.

Because of concentration difference holes or electron try to vary from their side to other side. Only these holes or electrons cross the junction, having high kinetic energy. This

Semiconductor is solid material whose electrical conductivity at room temperature lies between conductivity of a conductor and that of an insulator. At high temperatures its conduc

A modern turbofan engine in a commercial jet takes in air, part of which passes through the compressors, combustion chambers, and turbine, and the rest of which bypasses the compre

Who manufactures optical ports?  All system integrator generate a particular type of optical port to attach to their choice of illuminator.

Explain logarithmic decrement? Evaluate the ratio of nth amplitude with 1st amplitude in case of under damped oscillation.

When one is computing the electric potential at a particular point in space due to a continuous charge distribution what exactly is one calculating? Ans: The electric poten

Experiencing a constant horizontal 1.10 m/s wind, a hot-air balloon ascends from the launch site at a constant vertical speed of 2.70 m/s. At a height of 202 m, the balloonist main

SQUIDs, or super conducting Quantum interference devices are used to measure minute changes in magnetic flux by means of a pair of Josephson junctions, often used to detect extrem