How much time would it take to distribute one Avogadro number of wheat grains,

Avogadro number $=6.02 \times 10^{23}$

Thus, time required

$=\frac{6.02 \times 10^{23}}{10^{10}} \mathrm{~s}$

$=6.02 \times 10^{23} \mathrm{~s}$

$=\frac{6.02 \times 10^{23}}{60 \times 60 \times 24 \times 365}$ years

$=1.909 \times 10^{6}$ years

Hence, the time taken would be $1.909 \times 10^{6}$ years.