Respuesta :
Answer:
[tex]10^{42}[/tex]
Explanation:
- The mean lifetime of a top quark is of the order of [tex]10^{-25} s[/tex]
- The approximate age of the universe is 13.7 billion years, so in seconds:
[tex]13.7 \cdot 10^9 y \cdot 365 d \cdot 24 h \cdot 60 min \cdot 60 s=4.3\cdot 10^{17} s \sim 10^{17} s[/tex]
So, the ratio between the age of the universe and the lifetime of a top quark is:
[tex]r=\frac{10^{17} s}{10^{-25} s}=10^{42}[/tex]
The total number of quark lifetimes that have occurred all through the life of universe is around [tex]\boxed{10^{42}\text{ lifetimes}}[/tex].
Explanation:
The universe is considered to be formed from the big bang take took place in the space several billion years ago. The approximate age of the universe is considered to be almost [tex]13.7\text{ billion years}[/tex].
The quarks are considered to be the sub-atomic particles that have some charge and have a very small life time of about [tex]10^{-25}\text{ s}[/tex].
The total lifetime of the universe can be expressed in terms of seconds as:
[tex]\begin{aligned}T&=13.7\times10^{9}\text{ years}\left(\dfrac{365\text{ days}}{1\text{ year}}\right)\left(\dfrac{24\text{ hrs}}{1\text{ day}}\right)\left(\dfrac{60\text{ min}}{1\text{ hr}}\right)\left(\dfrac{60\text{ sec}}{1\text{ min}}\right)\\&=13.7\times10^{9}\times365\times24\times60\times60\text{ sec}\\&=4.32\times10^{17}\text{ sec}\end{aligned}[/tex]
Since the lifetime of a quark is very small, the total lifetime that have occurred during the life of the universe can be obtained as the ratio of the total life of universe to the total lifetime of one quark.
Write the expression for the number of lifetimes of quarks as:
[tex]\boxed{n=\dfrac{T}{t}}[/tex]
Here, [tex]t[/tex] is the lifetime of a quark.
Substitute the value of the lifetime of universe and that of the quark in above expression.
[tex]\begin{aligned}n&=\dfrac{4.32\times10^{17}\text{ sec}}{10^{-25}\text{ sec}}\\&\approx10^{42}\text{ lifetimes}\end{aligned}[/tex]
Therefore, the number of lifetimes of quarks occurred over the lifetime of universe is almost [tex]\boxed{10^{42}\text{ lifetimes}}[/tex].
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Answer Details:
Grade: High School
Subject: Physics
Chapter: Units and Measurement
Keywords:
quarks, time, lifetime, history of universe, big bang, space, 13.7 billion years, number of lifetimes.
