5. You will need the following bits of information to solve this problem: • Noth

Question

5. You will need the following bits of information to solve this problem: • Nothing can move faster than the speed of light, which is about c=3x108 m/sec. (More precisely, the latest/best measurement indicates it is 299,792,458 m/sec, but for the purposes of this question, just assume c=3x108 m/sec.) • The radius of the observable universe is about 13.8 billion light years. (It is actually bigger because it keeps expanding, but we can’t see exactly what has happened to the most distant galaxies over the last 13.8 billion years. Perhaps you can estimate the rate of expansion and recalculate this in EGR 201.) • The Diameter of a free proton is about d=1.7x10-15 m, or about 1.7 fm. 5a.What is the radius, in yottameters, Ym, of the observable universe? (A year consists of 31.558 Msec, or 31.558x106 sec, so a light year is 300 Mm/sec multiplied by 31.558 Msec. Work this out, and you should get 1 Light Year is equal to about 9.46 Pm.) 5b.How long does it take for a particle travelling at the speed of light to traverse the diameter of a proton? (Remember, time=distance/speed.) Present your answer in yoctoseconds, ysec

Explanation / Answer

5a) radius of universe = 13.8 billion light years

= 13.8*10^9*(c*year)

= 13.8*10^9*3*10^8*364*24*60*60

= 1.302*10^26 m

= 130.2*10^24 m

= 130.3 yotta m (yotta = 10^24)

5 b)

time taken = distance travelled/speed

= pi*d/c

= pi*1.7*10^-15/(3*10^8)

= 1.78*10^-23 s

= 0.178*10^-24 s

= 0.178 yocto s (yocto = 10^-24 )

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