## It's a Wonderful Line: Data Analysis Using Graphs

##### Conservation Laws - Data Analysis Using Graphs - Histograms - Units or Vectors in Particle Physics Example 1 - Example 2 - Example 3 - Example 4 - Problems
Try some on your own. . . .
Try to solve each problem by graphing the data and analyzing the graph. You may see the data here and download the tables with accompanying initial graphs as an MS Excel file graphqs.xls.
1. In a photolectric effect experiment, the energies of photoelectrons emitted from a sodium sample seems to depend on the frequency of incident light. Find an equation for energy E as a function of frequency f using either the data below or in Sheet 1, graphqs.xls.

 frequency f of incident light (x 1014 Hz) photoelectron energy E (eV) 5.5 0 5.75 0.11 6.00 0.21 6.25 0.31 6.50 0.42 6.75 0.52 7.00 0.62 7.25 0.73 7.50 0.83 7.75 0.93 8.00 1.04

2. When a beam of charged particles is accelerated into a circular path, whether in a cyclotron or an synchrotron like the Tevatron, it will produce electromagnetic radiation called synchrotron radiation. Many accelerators are designed for just this purpose.

Examples: National Synchrotron Light Source at Brookhaven National Laboratory and SPring-8 in Japan.

QuarkNet teachers recently traveled to several fictional synchrotron facilities and took data on their radii and the energy of the emitted radiation, normalized to a 10 GeV beam. Find a relationship between radiated synchrotron energy E and radius R using the data below or Sheet 2, graphqs.xls.

 radius R (km) radiated energy E (MeV) 0.2 4.38 .4 2.20 0.6 1.45 0.8 1.15 1.0 0.84 1.2 0.70 1.4 0.63 1.6 0.59 1.8 0.46 2.0 0.48

3. The data below compares the atomic masses of elements in atomic mass units (amu) to their nuclear radii in picometers (pm). Derive a relationship between radius R and atomic mass M using the data below or in Sheet 3, graphqs.xls.

 Element Atomic Mass M (amu) Nuclear Radius R (pm) He 4 0.0019 Be 9 0.0024 C 12 0.0027 N 14 0.0028 O 16 0.0030 Al 27 0.0036 Fe 56 0.0045 Ga 70 0.0049 Br 80 0.0051 Cs 133 0.0061 W 184 0.0068 Pb 208 0.0071 U 238 0.0074

4. A counter is used to measure incoming pions from a beam. The pions are slowed by an energy-absorbing material in the counter. Their decays are then recorded and timed so that, with a little manipulation, data is available on how many pions in an intial group of about 400 exist after 5 nanoseconds (ns), 10 ns, 15 ns, and so on. Find the lifetime of this sort of pion using the data beow or in Sheet 4, graphqs.xls.

 Time t (ns) Counts N 0 400 5 330 10 272 15 224 20 185 25 152 30 126 35 104 40 85 45 70 50 58