The Standard Model explains how the basic building blocks of matter interact, governed by four fundamental forces - Scottish Highers Physics - Question 6 - 2022

The K+ particle is made up of an up quark (u) and an anti-strange quark (ar{s}).

The fundamental force involved in the decay of kaons is the weak nuclear force.

To calculate the time taken ($t$) for a pion to travel 30.0 m at a speed of 0.95c:

$t = \frac{d}{v} = \frac{30.0 \text{ m}}{0.95c}$

Since $c \approx 3.00 \times 10^8 \text{ m/s}$:

$t = \frac{30.0}{0.95 \times 3.00 \times 10^8} \approx 1.1 \times 10^{-7} \text{ s}$

Approximately 0.11 microseconds.

In the frame of reference of the pions, we apply the length contraction formula:

$L' = L \sqrt{1 - \frac{v^2}{c^2}}$

Where:

• $L = 30.0 m$ (the distance measured by the stationary observer)
• $v = 0.95c$

Calculating:

$L' = 30.0 \sqrt{1 - (0.95)^2} \approx 30.0 \sqrt{1 - 0.9025} \approx 30.0 \sqrt{0.0975} \approx 30.0 \times 0.3122 \approx 9.37 m$

In a pion's frame of reference, the mean lifetime is shorter than the 26 ns expected in a stationary observer's frame due to time dilation. Because the pions are moving close to the speed of light, they experience a longer lifetime relative to the stationary frame, allowing more pions to decay before reaching the second detector than anticipated without relativistic adjustments.

The analogy of the Standard Model resembling children's building blocks illustrates how fundamental particles combine to form complex matter structures, just as various shapes can create different structures. This helps to visualize the interactions and configurations that make up all matter.