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Found in: Page 1365

### Fundamentals Of Physics

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

# There is no known meson with charge quantum number ${\mathbf{q}}{\mathbf{=}}{\mathbf{+}}{\mathbf{1}}$ and strangeness ${\mathbf{S}}{\mathbf{=}}{\mathbf{-}}{\mathbf{1}}$ or with ${\mathbf{q}}{\mathbf{=}}{\mathbf{-}}{\mathbf{1}}$ and .${\mathbf{S}}{\mathbf{=}}{\mathbf{+}}{\mathbf{1}}$ Explain why in terms of the quark model.

Mesons with strangeness ${\mathbf{S}}{\mathbf{=}}{\mathbf{-}}{\mathbf{1}}$ can have charge${\mathbf{q}}{\mathbf{=}}{\mathbf{-}}{\mathbf{1}}{\mathbf{,}}{\mathbf{0}}$ and those strangeness role="math" localid="1663136410092" ${\mathbf{S}}{\mathbf{=}}{\mathbf{+}}{\mathbf{1}}$ can have charge ${\mathbf{q}}{\mathbf{=}}{\mathbf{1}}{\mathbf{,}}{\mathbf{0}}$

See the step by step solution

## Step 1: Given data

No meson has charge $q=+1$and strangeness $S=âˆ’1$ or charge$q=âˆ’1$ and strangeness.$S=+1$

## Step 2: Quantum numbers of quarks

The up, charm and top quarks and charge$q=2/3$ and the down, strange and bottom quarks have charge $q=âˆ’1/3$. The anti quarks have negative charges with magnitude same as those of the respective quarks. Only the strange quark has strangeness$S=âˆ’1$ and the anti strange has strangeness.$S=1$ The rest of the quarks have zero strangeness.

## Step 3: Determining the reason why mesons don't have charge q=+1  and strangeness S=-1  or chargeq=-1   and strangeness  S=+1

A meson is made up of one quark and one anti-quark. For a meson to have strangeness,$S=âˆ’1$ it must have a strange quark. The accompanying anti-quark can be anything except an anti-strange. If the anti-quark is an anti-up, anti-charm or anti-top, the net charge of the meson will be.$âˆ’\frac{2}{3}âˆ’\frac{1}{3}=âˆ’1$ If the anti-quark is an anti-down or anti-bottom the net charge of the meson will be.$\frac{1}{3}âˆ’\frac{1}{3}=0$ Thus, charge $q=+1$and strangeness $S=âˆ’1$ is not possible.

For a meson to have strangeness$S=1$, it must have an anti-strange quark. The accompanying quark can be anything except a strange quark. If the quark is a up quark, a charm or a top, the net charge of the meson will be$\frac{2}{3}+\frac{1}{3}=1$ . If the quark is a down or a bottom the net charge of the meson will be$âˆ’\frac{1}{3}+\frac{1}{3}=0$. Thus, charge$q=âˆ’1$ and strangeness is $S=+1$not possible.