Question

Scientists found that the ratio of the longest and shortest lengths of objects in our universe is about 10⁴¹. What can be the ratio of the longest and shortest time intervals associated with the events and objects in our universe?
1. 1041
2. 1021.
3. (1041) 2
4. None of the above

Answer 1

Correct Answer - Option 1 : 1041

CONCEPT:

• Scientists found that the ratio of the longest and shortest lengths of objects in our universe is about 10⁴¹.
• The ratio of the longest and shortest time intervals of different events and objects in our universe is also about 10⁴¹.
• Range and order of time intervals:

Event	Time interval
Life-span of most unstable particle	10-24
Time required for light to cross a nuclear distance	10-22
Period of x-rays	10-19
Period of atomic vibrations	10-15
Period of lightwave	10-15
The lifetime of an excited state of an atom	10-8
Wink of eye	10-1
Travel time for light from the moon to the Earth	102
The time period of satellite	104
Revolution period of the Earth	105
Average human life-span	109
Time since dinosaurs became extinct	1015
Age of the universe	1017

EXPLANATION:

• In our universe, the known largest time interval is the age of the universe and

Age of the universe = 10¹⁷ sec (longest time interval)

• The known smallest time interval in our universe is the life span of most unstable particles.

Age of the life span of most unstable particles = 10^-24 sec (Shortest time interval)

• So the ratio of longest and shortest time intervals 

 \(ratio= {Age~of~the~universe \over Age~ of~ the ~life ~span ~of ~most~ unstable~ particles}={10^{17} \over 10^{-24}}=10^{41}\)

So the correct answer is option 1.

• This number 10⁴¹ is very important because similarly,
• The ratio of the largest and smallest masses of the objects in our universe is about (10⁴¹ )².