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Half Life Formula

About Half Life Formula

The half-life formula is used to calculate the half-life of a decaying or reducing chemical. The rate of decomposition of a material varies depending on how much of the substance is present. The pace of decay slows as the quantity of the chemical decreases, making it difficult to determine the life of a decaying substance. As a result, the half-life formula is used to determine the appropriate metrics for defining the life of decaying material. Let's study more about the half-life formula and solve some cases in this part.

What is Half-Life Formula?

Half-life refers to time it takes for half of a sample to react, or the time it takes for a quantity to decline from its initial value to half of its value. In nuclear physics, the half-life formula is used to explain the rate at which an atom undergoes radioactive decay. The half-life formula is obtained by multiplying 0.693 by the constant. The disintegration or decay constant is defined here. As a result, the formula for calculating a substance's half-life is:

  • t1/2 = 0.693/λ
  • Where,
  • t1/2 = half-life
  • λ = constant

Half-Life Formula

Let N be the size of the radioactive atom population at a particular time t, and dN be the amount by which it shrinks over time dt. dN/dt = -λN is the rate of change, where N is the decay constant.
On integrating this equation, we get N = N0e-λt, where N0= the size of the initial population of radioactive atoms at t = 0.This shows that the population decays exponentially at a rate that depends on λ. The time taken for half the original population of radioactive atoms to decay is called the half-life. This relationship between half-life, the time period, t1/2, and the decay constant λ is given by t1/2 = 0.693/λ.

  • Nt = N0e-λt
  • No = initial quantity
  • Nt = quantity after time t
  • λ = decay constant
  • t = time period
  • Hence,

  • Nt = No/2
  • t = t1/2
  • No/2 = Noe-λt1/2
  • 1/2 = 1 : e-λt1/2
  • loge1/2 = λt1/2
  • t1/2 = loge2/λ
  • t1/2 = 0.693/λ

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