Derive the equation λ = \(\frac{(-\frac{dN}{dt})}N\) and write wha

1.	Derive the equation λ = \(\frac{(-\frac{dN}{dt})}N\) and write what does λ denotes.
Answer» The rate of decay of a radioelement at any instant is proportional to the number of nuclei (atoms) present at that instant. It can be represented as, \(-\frac{dN}{dt}\) ∝ N or \(-\frac{dN}{dt}\) = λN.....(i) Where, \(-\frac{dN}{dt}\) = Rate of decay at any time, t λ = Decay constant N = Number of nuclei (atoms) present at time, t From equation (i), λ = \(\frac{(-\frac{dN}{dt})}N\) or λ = \(-\frac{dN}{dt}\) x \(\frac{1}N\) Decay constant (λ) is the fraction of nuclei decaying in unit time. OR It is the ratio of the amount of substance disintegrated per unit time to the amount of substance present at that time.

Derive the equation λ = \(\frac{(-\frac{dN}{dt})}N\) and write what does λ denotes.

Answer»

The rate of decay of a radioelement at any instant is proportional to the number of nuclei (atoms) present at that instant. It can be represented as,

\(-\frac{dN}{dt}\) ∝ N or \(-\frac{dN}{dt}\) = λN.....(i)

Where, \(-\frac{dN}{dt}\) = Rate of decay at any time, t

λ = Decay constant

N = Number of nuclei (atoms) present at time, t

From equation (i),

λ = \(\frac{(-\frac{dN}{dt})}N\) or λ = \(-\frac{dN}{dt}\) x \(\frac{1}N\)

Decay constant (λ) is the fraction of nuclei decaying in unit time.

It is the ratio of the amount of substance disintegrated per unit time to the amount of substance present at that time.