A newly discovered particle, the SPARTYON, has a mass 895 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.
To determine the frequency of the emitted photons, we can use the principle of conservation of energy and apply Einstein's equation, E = mc^2, where E is the energy, m is the mass, and c is the speed of light.
Given that the mass of a SPARTYON is 895 times that of an electron, we can calculate the mass of a SPARTYON (m_SPARTYON) using the mass of an electron (m_electron):
m_SPARTYON = 895 * m_electron
The energy of a SPARTYON at rest can be calculated as:
E_SPARTYON = m_SPARTYON * c^2
To find the energy of the emitted photons, we need to consider the conservation of energy. When a SPARTYON and an anti-SPARTYON annihilate each other, their total energy is converted into the energy of the emitted photons.
Since the SPARTYON and the anti-SPARTYON have equal masses, the initial total energy is:
E_initial = 2 * m_SPARTYON * c^2
The energy of each emitted photon is given by:
E_photon = E_initial / 2
Finally, to calculate the frequency (f) of each emitted photon, we use the relation:
E_photon = h * f
Where h is the Planck constant.
Substituting the values into the equations:
m_SPARTYON = 895 * (9.11×10^-31 kg) = 8.14945×10^-28 kg
E_SPARTYON = (8.14945×10^-28 kg) * (3 × 10^8 m/s)^2 = 7.334505×10^-11 J
E_initial = 2 * (8.14945×10^-28 kg) * (3 × 10^8 m/s)^2 = 4.40067×10^-10 J
E_photon = (4.40067×10^-10 J) / 2 = 2.200335×10^-10 J
Using the Planck constant, h = 6.63 × 10^-34 J·s:
f = E_photon / h = (2.200335×10^-10 J) / (6.63 × 10^-34 J·s)
f ≈ 3.3259 × 10^23 Hz
Since the answer is in Hz, to convert it to 10^20 Hz (1020 Hz), we divide by 10^3:
f = (3.3259 × 10^23 Hz) / (10^3) = 3.3259 × 10^20 Hz
Therefore, the frequency of each emitted photon is approximately 3.3259 × 10^20 Hz.