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Chapter 3: Problem 11

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 \(6.0 \times 10^{23}\) particles? Assume that there are 365 days in a year.

Short Answer

Expert verified
It would take approximately \(1.46 \times 10^6\) or 1,460,000 years for the entire Earth's population to count \(6.0 \times 10^{23}\) particles at the given rate.

Step by step solution

01

Analyze the Problem

The problem is to determine time. We know the rate at which each person can count particles (2 particles per second) and the number of particles to be counted \((6.0 \times 10^{23})\). We also know the Earth's population is \(6.5 \times 10^9\) (6.5 billion) people.
02

Convert Rate to Particles per Year

Each person counts 2 particles per second, so we need to convert that to particles per year. As there are \(60\) seconds in a minute, \(60\) minutes in an hour, \(24\) hours in a day, and \(365\) days in a year, each person counts \(2 \times 60 \times 60 \times 24 \times 365\) particles in a year. This is \(63,072,000\) particles annually per person.
03

Calculate Total Particles Counted per Year

Having the Earth's population is \(6.5 \times 10^9\), we can calculate the total number of particles that can be counted by the entire population each year by multiplying the population by the number of particles counted annually per person. This gives us \(6.5 \times 10^9 \times 63,072,000 = 4.1 \times 10^{17}\) particles per year.
04

Determine the Number of Years

Now, by dividing the total particles to count by the total number of particles the population can count each year, one can find the time needed. \(6.0 \times 10^{23} \div 4.1 \times 10^{17} = 1.46 \times 10^6\) years.

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