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

The group of matter particles that includes quarks and leptons is known as fermions.

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

ext{Total Charge} = 2 imes rac{2}{3} e + 1 imes (-rac{1}{3} e) + 1 imes rac{2}{3} e + 1 imes (-rac{2}{3} e)

Calculating this yields:

= rac{4}{3} e - rac{1}{3} e + rac{2}{3} e - rac{2}{3} e = 1 e

Thus, the total charge on the Λ_b pentaquark is +e.

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

To calculate the mean lifetime relative to a stationary observer, we use the time dilation formula:

t = rac{t_0}{eta} where eta = rac{v}{c}.

Here, $t_0 = 8.0 × 10^{-21}$ s and $v = 0.91c$, so eta = 0.91:

t = rac{8.0 × 10^{-21} ext{ s}}{0.91} ≈ 8.79 × 10^{-21} ext{ s}

Thus, the mean lifetime relative to the stationary observer is approximately $8.79 × 10^{-21}$ s.

To convert the mass-energy equivalence of the Λ_b pentaquark from MeV to joules:

$E = 4450 ext{ MeV} imes 1.60 × 10^{-19} ext{ J/eV}$

Calculating this gives:

$E = 4450 × 1.60 × 10^{-3} × 10^{-19} ext{ J} ≈ 7.12 × 10^{-16} ext{ J}$

Thus, the energy of the Λ_b pentaquark in joules is approximately $7.12 × 10^{-16}$ J.

Using the energy-mass equivalence relation:

$E = mc^2$ we can rearrange to find mass:

m = rac{E}{c^2} where $E = 7.12 × 10^{-16} ext{ J}$ and $c ext{ (speed of light)} ≈ 3 × 10^8 ext{ m/s}.$

Calculating this yields:

m ≈ rac{7.12 × 10^{-16}}{(3 × 10^8)^2} ≈ 7.91 × 10^{-33} ext{ kg}

Therefore, the mass of the Λ_b pentaquark is approximately $7.91 × 10^{-33}$ kg.