• :00Days
• :00Hours
• :00Mins
• 00Seconds
A new era for learning is coming soon

Suggested languages for you:

Americas

Europe

Q10Q

Expert-verified
Found in: Page 1362

### Fundamentals Of Physics

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

# As we have seen, the ${{\mathbf{\pi }}}^{\mathbf{-}\mathbf{1}}$ meson has the quark structure ${\mathbit{d}}\overline{\mathbf{u}}$ .Which of the following conservation laws would be violated if a ${{\mathbf{\pi }}}^{\mathbf{-}\mathbf{1}}$ were formed, instead, from a d quark and a u quark: (a) energy, (b)angular momentum, (c) charge, (d) lepton number, (e) linear momentum,(f) baryon number?

(a) The energy conservation law will not be violated.

(b) The angular momentum conservation law will not be violated.

(c) The charge conservation law will be violated.

(d) Lepton number conservation law will not be violated.

(e) The linear momentum conservation law will not be violated

(f) The baryon number conservation law will be violated.

See the step by step solution

## Step 1: Identifying the data given in the question

The quark structure of ${\pi }^{-}$ meson is $d\overline{\mathrm{u}}$

## Step 2: Concept used to solve the question

Quarks and Mesons

Mesons are hadronic subatomic particles in particle physics that are made up of an equal number of quarks and antiquarks, typically one of each, and are joined by strong interactions.

Instead of a $\overline{\mathrm{u}}$ quark, we are considering a u quark. So, we just need to consider the properties of $\overline{\mathrm{u}}$ and u which are different.

## Step 3:(a) Energy conservation law

According to the energy conservation

The energy of $\overline{\mathrm{u}}$ quark = Energy of a u quark

Energy can be given as

$E=m{c}^{2}$

Where E is energy, m is mass, c is the velocity of light.

The rest mass of u quark

${m}_{u}=10\mathrm{MeV}/{\mathrm{c}}^{2}\phantom{\rule{0ex}{0ex}}{\mathrm{m}}_{\overline{)\mathrm{u}}}=10\mathrm{MeV}/{\mathrm{c}}^{2}$

Because the rest mass of the particle and its antiparticle is the same therefore energy corresponding to them will be the same so the energy conservation law will not be violated.

## Step 4:(b) Angular momentum

According to the angular momentum conservation

The spin of $\overline{\mathrm{u}}$ quark = The spin of a u quark

Because the spin of a particle and its antiparticle is the same therefore spin angular momentum corresponding to them will be the same so the angular momentum conservation law will not be violated.

## Step 5:(c) Charge

According to the charge conservation

The charge of $\overline{\mathrm{u}}$ quark = The charge of a u quark

Because the charge of a particle and its antiparticle are opposite, so the charge conservation law will be violated

## Step 6:(d) Lepton number

According to the lepton number conservation

lepton number of $\overline{\mathrm{u}}$ quark = Lepton number of a u quark

Since all the quarks have lepton number zero.

Because the lepton number of a particle and its antiparticle are the same, so the lepton number conservation law will not be violated.

## Step 7:(e) linear momentum

According to the linear momentum conservation

Linear momentum of $\overline{\mathrm{u}}$ quark = linear momentum of a u quark

Because the direction of both the particle and its antiparticle is upward, therefore, linear momentum corresponding to them will be the same so the linear momentum conservation law will not be violated

## Step 8:(f) Baryon number

According to the Baryon number conservation

Baryon number of $\overline{\mathrm{u}}$ quark = Baryon number of a u quark

Baryon number of a u quark is $+\frac{1}{3}$

Baryon number of $\overline{\mathrm{u}}$ quark is $-\frac{1}{3}$

Because the baryon number of a particle and its antiparticle are different, so the baryon number conservation law will be violated.

## Recommended explanations on Physics Textbooks

94% of StudySmarter users get better grades.