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Found in: Page 1365

### Fundamentals Of Physics

Book edition 10th Edition
Author(s) David Halliday
Pages 1328 pages
ISBN 9781118230718

# A particle game. Figure 44-13 is a sketch of the tracks made by particles in a fictional cloud chamber experiment (with a uniform magnetic field directed perpendicular to the page), and Table 44-6 gives fictional quantum numbers associated with the particles making the tracks. Particle A entered the chamber at the lower left, leaving track and decaying into three particles. Then the particle creating track 1 decayed into three other particles, and the particle creating track 6 decayed into two other particles, one of which was electrically uncharged—the path of that uncharged particle is represented by the dashed straight line because, being electrically neutral, it would not actually leave a track in a cloud chamber. The particle that created track is known to have a seriousness quantum number of zero. By conserving the fictional quantum numbers at each decay point and by noting the directions of curvature of the tracks, identify which particle goes with track (a) 1, (b) 2, (c) 3, (d) 4, (e) 5, (f) 6, (g) 7, (h) 8, and (i) 9. One of the listed particles is not formed; the others appear only once each.ParticleChargeWhimsySeriousnessCuteness A 1 1 -2 -2 B 0 4 3 0 C 1 2 -3 -1 D -1 -1 0 1 E -1 0 -4 -2 F 1 0 0 0 G -1 -1 1 -1 H 3 3 1 0 I 0 6 4 6 J 1 -6 -4 -6

(a) The particle corresponding to track ${\mathbf{1}}$ is ${\mathbit{A}}$.

(b) The particle corresponding to track ${\mathbf{2}}$ is ${\mathbit{J}}$.

(c) The particle corresponding to track ${\mathbf{3}}$ is ${\mathbit{I}}$ .

(d) The particle corresponding to track ${\mathbf{4}}$ is ${\mathbit{F}}$.

(e) The particle corresponding to track ${\mathbf{5}}$ is ${\mathbit{G}}$.

(f) The particle corresponding to track ${\mathbf{6}}$ is ${\mathbit{C}}$.

(g) The particle corresponding to track ${\mathbf{7}}$ is ${\mathbit{H}}$.

(h) The particle corresponding to track ${\mathbf{8}}$ is ${\mathbit{D}}$.

(i) The particle corresponding to track ${\mathbf{9}}$ is ${\mathbit{E}}$.

See the step by step solution

## Step 1: Given data

Fictional quantum numbers of particles A to J are provided in the given table.

Track 1 corresponds to particle A.

Uncharged particles are dashed lines.

Particle corresponding to track 8 has zero seriousness.

## Step 2: Deviation of charged particles in the cloud chamber

Positive and negatively charged particle deviate in opposite directions in the cloud chamber.

## Step 3: Determining the particles corresponding to all the tracks

It is given that particle A produced track 1. Particle A is positively charged. Thus all tracks deviating left correspond to positively charged particles and all tracks deviating right correspond to negatively charged particles.

There are two particles with zero seriousness in the table, D and F. Track 8 deviates to the right and thus corresponds to a negatively charged particle. Hence

$8\equiv D$

Track 6 corresponds to a positively charged particle that decays to track 7 (positively charged), particle that is negatively charged and track 9 (negatively charged). From the table, this is only possible if the particle causing track has charge and particle corresponding to track 7 has +1 charge. Thus

$7\equiv H$

Track 3 corresponds to an uncharged particle. So it can be either B or I. Tracks 2 and 4 correspond to positively charged particles. If track 3 corresponds to B, cuteness quantum number of B is zero. Hence cuteness quantum numbers of particles producing tracks 2 and 4 should be the same. But none of the remaining positively charged particles have the same cuteness quantum numbers. Thus

$3\equiv I$

Particle I has cuteness 6. The only combination to conserve cuteness in that decay channel is to have cuteness of particle producing track 2 as -6(J) and that of track 4 as 0(F)

Thus

$\begin{array}{l}2\equiv J\\ 4\equiv F\end{array}$

The only positively charged particle left in the table is C and track 6 corresponds to a positively charged particle. Thus $6\to 7$

$6\equiv C$

In the decay channel $6\to 7+8+9$, that is $C\to H+D+9$, cuteness of C, H and D are -1,0 and 1 respectively. Thus the cuteness of particle creating track 9 should be $-1-0-1=-2$and should be negatively charged. The only negatively charged particle with -2 cuteness is E. Thus$9\equiv E$

Track 5 corresponds to a negatively charged particle and the only negatively charged particle left is G. Thus$5\equiv G$