Question

Earth’s population is about 6.5 billion. Suppose that
every person on Earth participates in a process of
counting identical particles at the rate of two particles per second. How many years would it take to count
6.0 3 1023 particles? Assume that there are 365 days
in a year.

Answer 1

Total population of Earth = 6.5 billion = 6.5x10⁹ people

Given each people counts 2 particles per second.

Total seconds in 1 year = 1 year x (365 day/1 year) x (24 hr / 1 day) x (60 min / 1 hr) x (60 s / 1 min)

= 365x24x60x60 s = 31536000 s

Hence number of particles counted by 1 person per year = 31536000 s x 2 particles / s

= 63072000 particles / people = 6.3072x10⁷ particles / people

Hence total number of particles counted by 6.5 billion people per year

= (6.3072x10⁷ particles / people) x 6.5x10⁹ people = 4.10x10¹⁷ particles / population /year

Hence number of years required to count 6.03x10²³ particles

= (1 / 4.10x10¹⁷ particles/year) x 6.03x10²³ particles = 1.471 x 10⁶ years or 1.471 million years (answer)