NEET Class neet Answered
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Asked by Prashant DIGHE | 10 Jan, 2020, 10:08: PM
Expert Answer
radioacivity depends on number of undecayed atoms present .
Hence in magnitude, dN/dt = λ N ..........................(1)
where dN/dt = activity or number of disintegration per unit time , λ is decay constant and
N is number of atoms present at time t .
we have radioactivity equation, N = No e-λt ...............(2)
Using eqn.(2), eqn.(1) is written as, dN/dt = λNo e-λt .................(3)
By taking natural logrithm on both side of eqn.(3), we get , ln( dN/dt ) = ln( λNo ) - λ t ................(4)
From eqn.(4), we know that, if ln ( dN/dt ) is plotted as a function of time, we get linear graph ( straight line ) with negative slope,
magnitude of slope gives decay constant λ .
we get slope from given graph as, λ = 0.5 (year)-1
using eqn.(2), we get decreasing factor of number of atoms for a priod of t years as, No / N = eλt
Hence decreasing factor for 4.16 years = ( No / N ) = exp( 4.16 × 0.5 ) = 8
Answered by Thiyagarajan K | 11 Jan, 2020, 11:56: AM
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