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Exercises · 5.14

Q.How much time would it take to distribute one Avogadro number of wheat grains, if 1010 grains are distributed each second ?

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Step 1 – Set up the division

Time=total grains to distributerate of distribution=NAgrains per second\text{Time} = \frac{\text{total grains to distribute}}{\text{rate of distribution}} = \frac{N_A}{\text{grains per second}}

Step 2 – Substitute

NA=6.022×1023,rate=1010 grains s−1N_A = 6.022\times10^{23}, \qquad \text{rate} = 10^{10}\ \text{grains s}^{-1}

t=6.022×10231010=6.022×1013 st = \frac{6.022\times10^{23}}{10^{10}} = 6.022\times10^{13}\ \text{s}

Step 3 – Convert seconds to years for a physically meaningful answer

1 year≈365 days×24 h×3600 s=3.154×107 s1\ \text{year} \approx 365\ \text{days} \times 24\ \text{h} \times 3600\ \text{s} = 3.154\times10^{7}\ \text{s} …

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