A newly discovered particle, the SPARTYON, has a mass 455 times that of an electron. If a SPARTYON at rest absorbs an anti-SPARTYON, what is the frequency of each of the emitted photons (in 1020 Hz)? The mass of an electron is 9.11×10-31 kg.

υ = 5.62 x 10¹⁴ Hz

Explanation:

The process of of formation of photons takes place due to interaction of a particle with its anti-particle is called Annihilation of Matter. Here SPARTYON absorbs anti-SPARYTON to form 2 photons. Applying conservation of energy to the to this scenario, we get:

2(Energy of Each Photon) = Rest Mass Energy of SPARTYON + Rest Mass Energy of anti-SPARTYON

where,

υ = frequency of each photon = ?

m₀ = rest mass of SPARTYON = mass of anti-SPARTYON = 455*Mass of electron

m₀ = 455(9.1 x 10⁻³¹ kg) = 4.14 x 10⁻²⁸ kg

c = speed of light = 3 x 10⁸ m/s

h = Plank's Constant = 6.625 x 10⁻³⁴ J.s

Therefore, using these values in the equation, we get:

υ = 5.62 x 10¹⁴ Hz

answer: the potential energy decreases from 379 j to 243 j

explanation:

for the law of conservation of energy, the total energy in a system must be conserved. the total energy of the system is given by the sum of kinetic (k) and potential (u) energy:

e = k + u

the total energy is e=675 j, and this does not change.

initially, the kinetic energy is k=296 j, so the potential energy is

at the end, the kinetic energy is k=432 j, so the potential energy is

so, we see that the potential energy has decreased from 379 j to 243 j.