Lab 9

Bubble Chamber Pictures

and

the Identification of Particles

 

 

 

 

Bill Chun Wai Hung

Marjan Montakhab

Nimish Kumar

 

Friday Section

 

21 June 2004


Data and Calculation:

Table 1.

Elements

h (cm)

l (cm)

r (cm)

mv (MeV/c)

E(MeV)

Pi-

5.7

30.6

84.9868421

764.881579

777.588471

Alpha

5

31.7

102.989

926.901

(Table 2)

Beta

4.4

17.5

37.0011364

333.010227

(Table 2)

Table 2.

Elements

Rest Energy (MeV)

Total Energy(MeV)

p

938

1318.7

pi+

140

937.4

k+

450

1030.4

pi-

140

361.2

k-

450

559.8

Table 3. Known Energy Values

E(pi-)(MeV)

E(p)(MeV)

E(pi-)+E(p)(MeV)

777.588471

938

1715.588471

Table 4. Guessed Alpha and Beta Energy Values

E(pi-)(MeV)

E(p)(MeV)

E(pi-)+E(p)(MeV)

361.2

1318.7

1679.9

 

Percentage Difference

 

Conclusion by Bill Chun Wai Hung:

In this experiment, we want to determine the identities of alpha and beta particles.

 

Since the centripetal force in this experiment is

Since in this bubble chamber case, the force is also a magnetic force, so

Reduce the equation gives

where r is in centimeters, B in kilogauss=30.0kG(kilogauss) in this case, and p in MeV/c.

By measuring the diagram, r can be calculated by the following equation

 

So the momentum and energy of the pion, alpha, and beta particle can be calculated by the following equations.

The experimental values of the momentum and energies of pion, alpha, and beta particles are

Elements

h (cm)

l (cm)

r (cm)

mv (MeV/c)

E(MeV)

Pi-

5.7

30.6

84.9868421

764.881579

777.588471

Alpha

5

31.7

102.989

926.901

(Table 2)

Beta

4.4

17.5

37.0011364

333.010227

(Table 2)

The percentage errors of the momentum are

Elements

Target mv (MeV/c)

Experimental mv (MeV/c)

% Difference

Pi-

900

764.881579

15.013158

Alpha

1089

926.901

14.885124

Beta

387

333.010227

13.950846

 

Since

and can be calculated by the equation

The results are

E(pi-)(MeV)

E(p)(MeV)

E(pi-)+E(p)(MeV)

777.588471

938

1715.588471

 

Therefore, should equals to 1715.6MeV

From the graph, the alpha particle bents left, while the beta particle bents right. So alpha might be positive particles like proton(p), pion positive(pi+), or Kaon positive (k+), while beta might be negative particles like pion negative (pi-) or Kaon negative (k-).

 

The table of possible alpha and beta particles is

Elements

Rest Energy (MeV)

Total Energy(MeV)

p

938

1318.7

pi+

140

937.4

k+

450

1030.4

pi-

140

361.2

k-

450

559.8

 

The total energy of  should equals to 1715.6MeV, so alpha particle is likely to be a proton, and beta particle is likely to be a pion negative.

 

Calculating  by the equation , we have

E(alpha)(MeV)

E(beta)(MeV)

E(alpha)+E(beta)(MeV)

361.2

1318.7

1679.9

 

1715.6MeV is supposed to be equal to 1679.9MeV (the total energy of our guess) calculated, but this is the best guess with the data obtained. The values are off because of the errors discussed below. The percentage error for this energy calculation is 2.08%

 

Error Analysis

The values are off because of the measurement of the curving path of the particle are off by about +-1cm. That is off by the measurement of l, h, and r.

 

The values are off also because the value of momentum we used are only accurate to 3 or 4 significant digits, that gives us an error in the calculation of the energy