Derive the relationship between half life and decay constant of a radioelement.
Derive the relationship between half life and decay constant of a radioelement.
7 views
1 Answers
Equation for the decay constant is given as,
λ = \(\frac{2.303}{t}\) log10\(\frac{N_0}{N}\) …(i)
Where,
λ = Decay constant
N = Number of nuclei (atoms) present at time t
At t = 0,
N = N0.
Hence,
At t = t1/2,
N = N0/2
Substitution of these values of N and t in equation (i) gives,
λ = \(\frac{2.303}{t_{1/2}}\) log10\(\frac{N_0}{\frac{N_0}{2}}\)
= \(\frac{2.303}{t_{1/2}}\)log102
= \(\frac{2.303}{t_{1/2}}\) x 0.3010
= \(\frac{0.693}{t_{1/2}}\)
Hence,
λ = \(\frac{0.693}{t_{1/2}}\) or t1/2 =\(\frac{0.693}{\lambda}\)
7 views
Answered