Chapter 11: Problem 52

What length track does a \(\pi^{+}\) traveling at \(0.100 c\) leave in a bubble chamber if it is created there and lives for \(2.60 \times 10^{-8} \mathrm{s} ?\) (Those moving faster or living longer may escape the detector before decaying.)

Short Answer

Expert verified

The length of the track left by a \(\pi^{+}\) traveling at \(0.100c\) in a bubble chamber, if it is created there and lives for \(2.60 \times 10^{-8}\) seconds, is approximately \(0.780\) meters.

Step by step solution

Convert the speed of the pi-meson to its SI unit (m/s)

Currently, the speed of the pi-meson is given as a fraction of the speed of light (\(0.100c\)). The speed of light is approximately \(3.0 \times 10^{8}\) m/s. Therefore, we first need to find the speed of the pi-meson in m/s. Speed of the pi-meson = \(0.100c = 0.100 \times 3.0 \times 10^{8}\) m/s

Calculate the length of the track left in the bubble chamber

Now that we have the speed of the pi-meson, we can use the formula mentioned earlier (Distance = Speed × Time) to calculate the length of the track left in the bubble chamber. Length of the track = Speed of the pi-meson × Time it lives Length of the track = \(0.100 \times 3.0 \times 10^{8} \times 2.60 \times 10^{-8}\) m

Simplify the expression

Next, we simplify the expression for the length of the track. Length of the track = \(0.100 \times 3.0 \times 2.60 \times 10^{8} \times 10^{-8}\) m Length of the track = \(0.780 \times 10^{0}\) m

Write the final answer

Finally, we write down the length of the track left by the pi-meson in the bubble chamber. Length of the track = \(0.780\) m So, the length of the track left by a \(\pi^{+}\) traveling at \(0.100c\) in a bubble chamber, if it is created there and lives for \(2.60 \times 10^{-8}\) seconds, is approximately \(0.780\) meters.

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What length track does a \(\pi^{+}\) traveling at \(0.100 c\) leave in a bubble chamber if it is created there and lives for \(2.60 \times 10^{-8} \mathrm{s} ?\) (Those moving faster or living longer may escape the detector before decaying.)

Short Answer

Step by step solution

Convert the speed of the pi-meson to its SI unit (m/s)

Calculate the length of the track left in the bubble chamber

Simplify the expression

Write the final answer

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