Question

If the average life of a person is taken as $100s$, the age of universe on this scale is of order
(A) ${10^{10}}s$
(B) ${10^8}s$
(C) ${10^{17}}s$
(D) ${10^9}s$

Answer 1

To solve this question, we need to use the average values of the universe and humans. We have to take the ratio of these two to get the scaling factor of the given scale. Multiplying the given age of humans with the scaling factor will give us the final answer.

Complete step-by-step solution:
We know that the age of the universe is approximately equal to $20$ billion years. So the age of the universe can be written as
${A_U} = 20 \times {10^9}y$
Now, we know that there are $365$ days in a year. So the age of the universe becomes
${A_U} = 20 \times {10^9} \times 365{\text{ days}}$
Now, there are $24$ hours in a day. Therefore the age of the universe now becomes
${A_U} = 20 \times {10^9} \times 365 \times 24h$
Finally, there are a total of $3600$ seconds in an hour. Thus, the age of the universe in seconds is given by
${A_U} = 20 \times {10^9} \times 365 \times 24 \times 3600s$
On solving we get
${A_U} = 6.31 \times {10^{17}}s$........................(1)
Therefore, the age of the universe is of the order of ${10^{17}}s$.
Now, we know that the average life of a person is approximately $79$ years. So the average human life can be written as
${A_H} = 79y$
By carrying out the same conversion as above, we get the average human life in seconds as
${A_H} = 79 \times 365 \times 24 \times 3600s$
On solving we get
${A_H} = 2.49 \times {10^9}s$..........................(2)
Therefore, the average life of a person is of the order of ${10^9}s$.
Now, we calculate the scaling factor of the given scale.
Dividing (1) by (2) we get
$\dfrac{{{A_U}}}{{{A_H}}} = 2.53 \times {10^8}$
As we are only considering the order of the age, so we consider the order of this ratio. Therefore we get the scaling factor as
$\dfrac{{{A_U}}}{{{A_H}}} = {10^8}$
Now, according to the question, ${A_H} = 100s$. Substituting it above, we get
$\dfrac{{{A_U}}}{{100s}} = {10^8}$
$\Rightarrow {A_U} = {10^{10}}s$
Therefore, the age of the universe on this scale is of the order ${10^{10}}s$.

Hence, the correct answer is option A.

Note: Even if we do not remember the exact value of the average ages of humans and the universe, we can still attempt this question correctly. We just need to be familiar with the order of the ages, that’s it. From the order only we can get the correct scaling factor, from which the required order of age can be calculated.