|
Remember the equation of the
hyperbola:
time2 - space2 =
constant
For the first data point, the equation becomes
(5.26699x10-12 s)2 -
(5.25320x10-12 s)2 = constant
1.4506x10-25 s2 = constant
The values of the
constant for all data points range from 6.5556x10-26 to 4.8848x10-25.
Every entry in the table, like all data, has some intrinsic,
unavoidable error. Each value of the constant calculated from the entries
is error-prone as well. Taking the average of many points helps to
minimize these errors.
The range of the calculated values for the constant may seem large
until you realize that the values are all within a power of ten. The
numbers have an average of
1.8450x10-25 ±
1.0248x10-25 s2.
Keep going!
|
|
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
|
|