Scientists have recently discovered a type of particle called a pentaquark - Scottish Highers Physics - Question 7 - 2019

The name given to the group of matter particles that contains quarks and leptons is Fermions.

To calculate the total charge on the Λ₆ pentaquark, we sum the charges of each quark:

• Charge from 2 up quarks: 2 × (+2/3) = +4/3
• Charge from 1 down quark: 1 × (-1/3) = -1/3
• Charge from 1 charm quark: 1 × (+2/3) = +2/3
• Charge from 1 anti-charm quark: 1 × (-2/3) = -2/3

Now, summing these:

$ext{Total charge} = (+4/3) + (-1/3) + (+2/3) + (-2/3) = +3/3 = +1$

Thus, the total charge on the Λ₆ pentaquark is +1.

The type of particle that is made of a quark-antiquark pair is called a Meson.

To find the mean lifetime of the quark-antiquark pair as observed by a stationary observer, we apply time dilation from special relativity:

$t' = t \sqrt{1 - \frac{v^2}{c^2}}$

Where:

• $t = 8.0 \times 10^{-21} \, \text{s}$ (the proper lifetime)
• $v = 0.91c$

Substituting values into the equation: $t' = 8.0 \times 10^{-21} \sqrt{1 - (0.91)^2}$ Calculating: $t' = 8.0 \times 10^{-21} \sqrt{1 - 0.8281} = 8.0 \times 10^{-21} \sqrt{0.1719} \approx 8.0 \times 10^{-21} \times 0.4142 \approx 3.31 \times 10^{-21} \, \text{s}$

So the mean lifetime relative to the stationary observer is approximately $3.31 \times 10^{-21} \, \text{s}$.

To calculate the energy of the Λ₆ pentaquark in joules, we use the mass-energy equivalence:

$E = mc^2\,$

Where:

• $m = 4450 \, \text{MeV} \times 1.60 \times 10^{-19} \, \text{J/eV} = 7.12 \times 10^{-16} \, \text{J}$.

So, the energy of the Λ₆ pentaquark is approximately $7.12 \times 10^{-16} \, \text{J}$.

To find the mass of the Λ₆ pentaquark, we use the energy calculated previously and apply the relation $E = mc^2$: Given $E = 4450 \, \text{MeV} = 7.12 \times 10^{-16} \, \text{J}$ and $c \approx 3.0 \times 10^8 \, \text{m/s}$:

$m = \frac{E}{c^2} = \frac{7.12 \times 10^{-16} \, \text{J}}{(3.0 \times 10^8 \, \text{m/s})^2} \approx 7.91 \times 10^{-33} \, \text{kg}$

Thus, the mass of the Λ₆ pentaquark is approximately $7.91 \times 10^{-33} \, \text{kg}$.