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Chapter 44: Q52P (page 1368)

Calculate the difference in mass, in kilograms, between the muon and pion of Sample Problem 44.01.

Short Answer

Expert verified

The difference in mass between the pion and muon is $6.03 \times 10^{- 29} kg$ .

Step by step solution

01

Given data

The interaction provided is

$π^{+} \to μ^{+} + ν$

02

Rest mass of muon and pion

The muon rest mass is

$m_{0 μ} = 105.7 MeV / c^{2} . . . . . . . 1$

The pion rest mass is

role="math" localid="1663137427708" $m_{0 π} = 139.6 MeV / c^{2} . . . . . . . . 2$

Here, c is the speed of light in vacuum with value

$c = 3 \times 10^{8} m / s$

03

Determining the difference in masses of muon and pion

From equations (I) and (II), the difference in the masses of muon and pion are

$m_{0 π} - m_{0 μ} = 139.6 {MeV/c}^{2} - 105.7 {MeV/c}^{2} = \frac{33.9}{{(3 \times 10^{8})}^{2}} \cdot (1 MeV \times \frac{1.602 \times 10^{- 13} kg \cdot m^{2} {/s}^{2}}{1 MeV}) \cdot (\frac{1}{1 m^{2} {/s}^{2}}) = 6.03 \times 10^{- 29} kg$

Thus, the difference is $= 6.03 \times 10^{- 29} kg$ .

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Most popular questions from this chapter

Certain theories predict that the proton is unstable, with a half-life of about 10³² years. Assuming that this is true, calculate the number ofproton decays you would expect to occur in one year in the water ofan Olympic-sized swimming pool holding 4.32 x 10⁵L of water.

The wavelength at which a thermal radiator at temperature $T$ radiates electromagnetic waves most intensely is given by Wien’slaw:localid="1663130298382" $λ_{m a x} = (2898 μ m . K) / T$ (a) Show that the energy $E$ of a photon corresponding to that wavelength can be computed from

$E = (4 .28 \times 10^{- 10} \frac{MeV}{K}) T$

(b) At what minimum temperature can this photon create an electron-positron pair(as discussed in Module 21-3)?

What quark combination is needed to form (a) and (b) $Ε^{0}$

Consider the neutrino whose symbol is $\bar{ν_{τ}}$ . (a) Is it a quark, a

lepton, a meson, or a baryon? (b) Is it a particle or an antiparticle? (c) Is it a boson or a fermion? (d) Is it stable against spontaneous decay?

Which conservation law is violated in each of these proposed reactions and decays? (Assume that the products have zero orbital angular momentum.)

$(a) \land^{0} \to {pK}^{-}; (b) Ω^{-} \to \sum_{}^{-} + π^{0} (S = - 3, q = - 1, m = 162 MeV / c^{2}, and m_{s} = \frac{3}{2} forΩ); (c) K^{-} + p \to \land 0 + π^{+}$

See all solutions

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