A bacterium weights about 1012g and can divide every 20 minu

A bacterium weights about 10^-12g and can divide every 20 minutes. If a single bacterial cell carried on dividing at this rate, how long would it take before the mass of bacteria would equal that of the Earth (6 x 10^24kg)? Contrast your result with the fact that bacteria originated at 3.5 billion years ago and have been dividing ever since. Explain the apparent paradox. How many bacteria will it take for their mass to equal the mass of Earth? How long (in hours) would it take before bacterial mass equals the mass of Earth? How many bacterial generations has the Earth actually seen? Can you provide a brief plausible explanations for the apparent paradox?

1. A bacterium weights about 10-12g and can divide every 20 minutes. If a single bacterial cell carried on dividing at this rate, how long would it take before the mass of bacteria would equal that of the Earth (6 x 10 kg)? Contrast your result with the fact that bacteria originated at 3.5 billion years ago and have been dividing ever since. Explain the paradox, (The number of cells N in a culture at time is described by the equation N No 2 where number of cells at zero time and G is the population doubling time.) How many bacteria will it take for their mass to equal the mass of Earth? How long (in hours) would it take before bacterial mass equals the mass of Earth? How many bacterial generations has the Earth actually seen? Can you provide a brief plausible explanation for this apparent paradox?

Solution

we know,

N=N₀ x 2ⁿ ; n=t/G

N= Final number of bacteria

N_{0= Initial number of bacteria}

n= no. of generations = total time/ time to double

Taking log both sides we finally get:

n = logN - logN₀ .......................(i)
           log2

Given,

Mass of earth = 6 x 10²⁴ kg

mass of one bacteria = 10^-12g =10^-15kg

so, total no. of bateria= 6 x 10²⁴ kg/10^-15kg =6x10³⁹ =N

Putting in (i)

n = log (6x10³⁹) - log 1   = 132.11 = (total time / time to double)

log2

Total time = 132.11 x 20 = 2642 minutes = 44.03 hours

Total life of earth = 3.5 billion years = 1.84 x 10¹⁵ minutes

total no. of generations earth has seen = 1.84 x 10¹⁵ / 20 = 9.2 x 10¹³ generations