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

The group of matter particles that contains quarks and leptons is called Fermions.

To calculate the total charge, we sum the charges of all the quarks in the \Lambda pentaquark:

• Charge from 2 up quarks:

  $2 \times +\frac{2}{3} e = +\frac{4}{3} e$

• Charge from 1 down quark:

  $-\frac{1}{3} e$

• Charge from 1 charm quark:

  $+\frac{2}{3} e$

• Charge from 1 anticharm quark:

  $-\frac{2}{3} e$

Now adding them together gives:

$+\frac{4}{3} e - \frac{1}{3} e + \frac{2}{3} e - \frac{2}{3} e = +1 e$

Thus, the total charge on the \Lambda pentaquark is +1 e.

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

To calculate the mean lifetime in the stationary observer's frame, we utilize time dilation. The formula is:

$t' = \frac{t_{0}}{\sqrt{1 - \frac{v^2}{c^2}}}$

Where:

• $t_{0} = 8.0 \times 10^{-21} s$ (proper time)
• $v = 0.91c$

Substituting in the values gives:

$t' = \frac{8.0 \times 10^{-21} s}{\sqrt{1 - (0.91)^2}}$

Calculating this results in the dilated mean lifetime in the stationary observer's frame.

To convert the mass-energy of the \Lambda pentaquark from MeV to joules, we use the conversion factor:

$E = 4450 \text{ MeV} \times 1.60 \times 10^{-19} \text{ J/eV}$

Calculating this gives:

$E = 4450 \times 1.60 \times 10^{-19} = 7.12 \times 10^{-16} \text{ J}$

Using the energy-mass equivalence formula $E = mc^2$, we first rearrange to find $m$:

$m = \frac{E}{c^2}$

Substituting the energy we found:

$m = \frac{7.12 \times 10^{-16} J}{(3.00 \times 10^8 m/s)^2}$

Calculating gives:

$m \approx 7.91 \times 10^{-19} kg$