Question

How many years would it take you to count and Avogadro’s number of objects if you could count at the rate of five objects per second?

Answer 1

Avogadro's number is $6.022 \times 10^{23}$

So the number of objects you want to count is $6.022 \times 10^{23}$

If you count them at a rate of 5 objects per second, it'd take;

$\dfrac{6.02 \times 10^{23} \textsf{ objects}}{5 \textsf{ objects per second}}$

$=1.2046 × 10^{23}\, s$

$1 \textsf{ year} = 60 \textsf{ seconds per minute} × 60 \textsf{ minutes per hour} × 24 \textsf{ hours per day} × 365 \textsf{ days per year}\\ =31536000 \textsf{ seconds}\\ =3.1536 × 10^7 \textsf{ seconds}$

$\therefore \textsf{number of years} = \dfrac{1.2046 × 10^{23}\, s}{3.1536 × 10^7 \textsf{ seconds per year}}$

$= 3.82 × 10^{15} \textsf{ years}$

$= 382,000,000,000,000 \textsf{ years}$

$= 382,000,000,000,000 \textsf{ trillion years}$