From the definition of the decay constant for nuclear decay, derive the exponential decay equation.

By definition, dn/dt = - λ N ,
If you separate the variables which contain N and t, and then integrate w.r.t N and w.r.t t you get,
lnN = -λt + C (1),
To find the constant of integration, solve (1) by setting N(t = 0) = N0 . This gives a value of,
C = lnN0 ,
By then substituting the value for C into (1), and relying on the properties of logs and exponentials, the following steps occur,
lnN = -λt + lnN0 ,
ln(N/N0) = -λt,
N/N0 = e-λt ,
N = N0e-λt,

Answered by Jake P. Physics tutor

1903 Views

See similar Physics A Level tutors

Related Physics A Level answers

All answers ▸

How do you work out the direction and strength of the force on a current carrying wire in a magnetic field?


When red light is shone on a metal, regardless of the intensity of this light, no current will flow. However if blue light is shone on this metal a current will flow. Why does this occur?


A ball is hit horizontally at a height of 1.2 m and travels a horizontal distance of 5.0 m before reaching the ground. The ball is at rest when hit. Calculate the initial horizontal velocity given to the ball when it was hit.


For 100ml of a liquid with a mass density of 1(kg m^-3), and a specific heat capacity of 2(kJ kg^-1 K^-1), how much energy is required to increase the temperature of the liquid by 4 degrees celsius. Assume no heat loss and that the liquid does not boil.


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences