|
The table contains Fermilab data, but the distance units are
"conventional." You can convert these distances to seconds by
using the speed of light as a conversion factor. Using D = vt, the
first decay length in the table becomes:
1.57487x10-03 m =
299,792,458 m/s x 5.2531x10-12
s
Convert the
entire table.
Note that the velocities are now unitless! Remember that velocity is a
ratio of distance to time. Because both distance and time are expressed in
seconds, their ratio is unitless.
Once the data are converted, you can begin to work with the numbers
to see what the
hyperbolic function might yield.
|
|
Bin Number
|
Velocity (unitless)
|
Mean Decay Length (m)
|
Mean Decay Time (s)
|
|
1
|
0.99738
|
1.57487 E-03
|
5.26699 E-12
|
|
2
|
0.99829
|
3.57708 E-03
|
1.19523 E-11
|
|
3
|
0.99883
|
3.33329 E-03
|
1.11317 E-11
|
|
4
|
0.99915
|
3.46872 E-03
|
1.15802 E-11
|
|
5
|
0.99936
|
4.17245 E-03
|
1.39267 E-11
|
|
6
|
0.99949
|
4.09255 E-03
|
1.36582 E-11
|
|
7
|
0.99960
|
5.07204 E-03
|
1.69254 E-11
|
|
8
|
0.99966
|
4.48678 E-03
|
1.49713 E-11
|
|
9
|
0.99972
|
4.75166 E-03
|
1.58543 E-11
|
|
10
|
0.99977
|
6.00550 E-03
|
2.00369 E-11
|
|
11
|
0.99980
|
4.03001 E-03
|
1.34454 E-11
|
|
12
|
0.99982
|
5.58903 E-03
|
1.86463 E-11
|
|
13
|
0.99985
|
5.67351 E-03
|
1.89277 E-11
|
|
14
|
0.99987
|
4.67871 E-03
|
1.56086 E-11
|
|
15
|
0.99988
|
6.11959 E-03
|
2.04153 E-11
|
|
16
|
0.99989
|
7.55170 E-03
|
2.51925 E-11
|
|
17
|
0.99990
|
1.16827 E-02
|
3.89732 E-11
|
|
18
|
0.99991
|
7.57815 E-03
|
2.52802 E-11
|
|