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Physics-

General

Easy

Question

Consider an initially pure M gm sample of ^AX, an isotope that has a half life of T hour, what is it’s initial decay rate (N_A= Avogrado No.)

$\frac{M N_{A}}{T}$
$\frac{0.693 M N_{A}}{T}$
$\frac{0.693 M N_{A}}{A T}$
$\frac{2.303 M N_{A}}{A T}$

The correct answer is: $fraction numerator 0.693 M N subscript A end subscript over denominator A T end fraction$

$N equals N subscript 0 end subscript e to the power of negative lambda t end exponent rightwards double arrow open vertical bar fraction numerator d N over denominator d t end fraction close vertical bar equals N subscript 0 end subscript lambda e to the power of negative lambda t end exponent$
Initially at t = 0, $open vertical bar fraction numerator d N over denominator d t end fraction close vertical bar subscript t equals 0 end subscript equals N subscript 0 end subscript lambda$
where N₀ = Initial number of undecayed atoms
$equals fraction numerator M a s s o f t h e s a m p l e over denominator M a s s o f a s i n g l e a t o m o f X end fraction equals fraction numerator M over denominator A divided by N subscript A end subscript end fraction equals fraction numerator M N subscript A end subscript over denominator A end fraction$
\ $open vertical bar fraction numerator d N over denominator d t end fraction close vertical bar subscript t equals 0 end subscript equals fraction numerator M N subscript A end subscript lambda over denominator A end fraction equals fraction numerator 0.693 M N subscript A end subscript over denominator A T end fraction$

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