Final answer:
The kinetic energy of a β ray traveling at 0.998c can be calculated using the relativistic kinetic energy formula. The correct answer is approximately 1000 MeV.
Step-by-step explanation:
The kinetic energy of a β ray traveling at 0.998c can be calculated using the relativistic kinetic energy formula:
Kinetic Energy (K) = (γ - 1)mc²
Where γ is the Lorentz factor given by:
γ = 1 / √(1 - (v/c)²)
In this case, v is the velocity of the β ray and c is the speed of light.
Plugging in the values, we get γ ≈ 22.36. Assuming the mass of the β ray is equal to the electron mass (9.11 × 10^-31 kg), and c = 3 × 10^8 m/s, we can calculate the kinetic energy:
Kinetic Energy = (22.36 - 1)(9.11 × 10^-31 kg)(3 × 10^8 m/s)² ≈ 2.06 × 10^-13 Joules ≈ 1.29 MeV
Therefore, the correct answer is (a) ≈ 1000 MeV.