Chapter 1, Problem 84A

To determine

Time taken (in years) by water droplet to evaporate.

Answer to Problem 84A

Almost 53 million years.

Explanation of Solution

Given:

Number of molecules in a water droplet= $1.7\times {10}^{21}$

Rate of evaporation= ${10}^6\text{molecules/s}$

Number of seconds in a day= $\text{8}\text{.64}\times {\text{10}}^4\text{s}$

Number of days in a year= $365=36.5\times {10}^2\text{days}$

Formula used:

  $\text{Time taken}=\frac{\text{number of molecules}}{\text{rate of evaporation}}$

Calculation:

Substitute the values and solve:

  $\begin{array}{c}t=\frac{1.7\times {10}^{21}}{{10}^6}\\ =1.7\times {10}^{15}\text{s}\end{array}$

  $\begin{array}{c}t=\frac{1.7\times {10}^{15}}{8.64\times {10}^4\times 3.65\times {10}^2}\\ =\frac{1.7}{31.54}\times {10}^9\\ =0.05389\times {10}^9\\ =53.89\times {10}^6\text{y}\end{array}$

Conclusion:

Time taken to evaporate is about 53 million years.