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GR9277 #49
Problem
 GREPhysics.NET Official Solution Alternate Solutions
\prob{49}
Two horizontal scintillation counters are located near the Earth's surface. One is 3.0 meters directly above the other. Of the following, which is the largest scintillator resolving time that can be used to distinguish downward-going relativistic muons from upwards-going relativistic muons using the relative time of the scintillator signals?

1. 1 picosecond
2. 1 nanosecond
3. 1 microsecond
4. 1 millisecond
5. 1 second

The maximal speed the muons can travel at is slightly less than c. Thus, since the distance is , the time required would be . The largest scintillator time is the one closest to this, which is 1 ns, as in choice (B).  Alternate Solutions
 epuma2013-10-09 01:16:57 Extremely fast relativistic muons will travel near the speed of light, c. Thus, we expect the minimum time for a muon to travel between the detectors to be on the order of 10 nanoseconds. t = d/v = 3m/c = 10ns The scintillator resolving time is the time between scintillator measurements. When the scintillator makes a measurement, it records which detectors have been triggered by a muon since the previous measurement. In order to distinguish which direction a muon has traveled, the scintillator must measure fast enough to 'see' the muon pass through each detector independently. Thus, the time between measurements must be less than the time required for the muon to travel between the detectors. In other words, the maximum scintillator resolving time must be less than 10ns. Choose (B)!Reply to this comment epuma
2013-10-09 01:16:57
Extremely fast relativistic muons will travel near the speed of light, c. Thus, we expect the minimum time for a muon to travel between the detectors to be on the order of 10 nanoseconds.

t = d/v = 3m/c = 10ns

The scintillator resolving time is the time between scintillator measurements. When the scintillator makes a measurement, it records which detectors have been triggered by a muon since the previous measurement. In order to distinguish which direction a muon has traveled, the scintillator must measure fast enough to 'see' the muon pass through each detector independently.

Thus, the time between measurements must be less than the time required for the muon to travel between the detectors. In other words, the maximum scintillator resolving time must be less than 10ns.

Choose (B)! evanb
2008-06-23 18:57:17
A useful fact is that c is just about 1 foot per nanosecond.

3 meters is about 10 feet, so the flight takes about 10 nanoseconds, so we have to be able to resolve on the order of 1 nanosecond to say for sure. SonOfOle
2006-11-02 23:29:58
The answer isn't (B) only because it's closest to 10^-8, but also because there must be more than one sample in the time it takes for the muon to pass through. Thus, the answer must also be less then 10^-8.
 elim2010-09-21 16:07:17 I agree to SonOfOle.. can someone explain what C is not right?
 alemsalem2010-09-25 07:49:03 to distinguish between up and down, you must be able to know for a given signal which detector went off first, since the muon is travelling at almost the speed of light (our assumption), the interval between the events (detections) is something like 10 to the minus 8,, detecting a time interval smaller than that is OK but detecting only larger intervals is no good,, so the largest OK resolving time is a nanosecond (B)      LaTeX syntax supported through dollar sign wrappers $, ex.,$\alpha^2_0$produces . type this... to get...$\int_0^\infty\partial\Rightarrow\ddot{x},\dot{x}\sqrt{z}\langle my \rangle\left( abacadabra \right)_{me}\vec{E}\frac{a}{b}\$