In a matter-antimatter annihilation event, a particle and its exact antiparticle completely disappear, releasing a total energy of 1.8 10¹⁴ J . The mass of a single particle is: (Take the speed of light c = 3 10^8 m/s )

Step-by-step solution

Let the mass of one particle be m . Since a particle and its antiparticle annihilate, the total mass converted into energy is 2m . Using Einstein's mass-energy equivalence: E = ( m)c^2 E = (2m)c^2 Given E = 1.8 10¹⁴ J and c = 3 10^8 m/s : 1.8 10¹⁴ = 2m (3 10^8)^2 1.8 10¹⁴ = 2m 9 10¹⁶ 2m = 1.8 10¹⁴ 9 10¹⁶ = 0.2 10⁻² kg = 2 10⁻³ kg Therefore, the mass of a single particle is: m = 1 10⁻³ kg Converting to grams: m = 1 10⁻³ 10^3 g = 1 g Answer: 1 g