Chapter 12: Q29E (page 557)

Table 12.1 gives the width of the K⁰ meson
(a) Approximately what is the its lifetime?.
(b) This meson’s actual radius is on the order 1 fm. Would its constituents have the time to bounce around inside a great deal?

Short Answer

Expert verified

(a) The lifetime of this particle is about $1 \times 10^{- 23} s$ .

(b)The constituents do not have enough time to bounce around inside.

Step by step solution

Given data

Width of $K^{* 0}$ mesons $= 51 MeV$

Concept of lifetime

The lifetime of this particle by the formula,

$τ = \frac{ℏ}{w i d t h}$

The distance dcan be expressed as:

$d = τ c$

Here c is the speed of light.

Step 3:Determine the lifetime of this particle

(a)

The width of $K^{* 0}$ is given to be $51 MeV$ , so the lifetime can be calculated as shown below.

$\begin{array}{rcl} τ & = & \frac{ℏ}{width} \\ = & \frac{1.055 \times 10^{- 34} J \cdot s}{51 MeV} (\frac{1 eV}{1.6 \times 10^{- 19} J}) \\ = & 1 \times 10^{- 23} s \end{array}$

Therefore, the lifetime of this particle is about $1 \times 10^{- 23} s$ .

Determine whether the constituents have the time to bounce around inside or not

(b)

Substitute $1 \times 10^{- 23}$ s for $τ$ and $3 \times 10^{8} m / s$ for c as:

$\begin{array}{rcl} d & = & (1 \times 10^{- 23} s) (3 \times 10^{8} m / s) \\ = & 3 \times 10^{- 15} m \\ = & 3 \times 10^{- 15} m (\frac{1 fm}{10^{- 15} m}) \\ = & 3 fm \end{array}$

The calculated value $3 \times 10^{- 15} m$ is less than that of the radius ( $1 fm$ ) of mesons.

Therefore, the constituents do not have enough time to bounce around inside.

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Table 12.1 gives the width of the K⁰ meson
(a) Approximately what is the its lifetime?.
(b) This meson’s actual radius is on the order 1 fm. Would its constituents have the time to bounce around inside a great deal?

Short Answer

Step by step solution

Given data

Concept of lifetime

Step 3:Determine the lifetime of this particle

Determine whether the constituents have the time to bounce around inside or not

One App. One Place for Learning.

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Table 12.1 gives the width of the K0 meson(a) Approximately what is the its lifetime?.(b) This meson’s actual radius is on the order 1 fm. Would its constituents have the time to bounce around inside a great deal?

Short Answer

Step by step solution

Given data

Concept of lifetime

Step 3:Determine the lifetime of this particle

Determine whether the constituents have the time to bounce around inside or not

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Mechanics and Materials

Fundamentals of Physics

Magnetism

Measurements

Physics of Motion

Particle Model of Matter

Study anywhere. Anytime. Across all devices.

Table 12.1 gives the width of the K⁰ meson
(a) Approximately what is the its lifetime?.
(b) This meson’s actual radius is on the order 1 fm. Would its constituents have the time to bounce around inside a great deal?