Find the relativistic momentum of an electron and proton accelerated through a potential of 10*10e6 Volts
10.5MeV/c , 137.4MeV/c
10.5MeV/c , 13.74MeV/c
105MeV/c , 13.74MeV/c
105MeV/c , 1.37MeV/c
None of the above
10.5Mev/c,137.4MeV/c
10
To find the relativistic momentum of an electron or proton accelerated through a potential, we can use the equation:
p = sqrt(2 * m * E)
Where p is the momentum, m is the mass of the particle, and E is the energy gained by the particle.
The mass of an electron is approximately 9.11 x 10^-31 kg, and the mass of a proton is approximately 1.67 x 10^-27 kg.
Given that the potential is 10 * 10^6 Volts, we can calculate the energy gained by the electron and proton:
For electrons:
E = e * V
E = 1.6 x 10^-19 C * 10 * 10^6 V
E = 1.6 x 10^-13 J
For protons:
E = e * V
E = 1.6 x 10^-19 C * 10 * 10^6 V
E = 1.6 x 10^-13 J
Now we can calculate the relativistic momentum for the electron and proton:
For electrons:
p = sqrt(2 * m * E)
p = sqrt(2 * 9.11 x 10^-31 kg * 1.6 x 10^-13 J)
p ≈ 10.5 MeV/c
For protons:
p = sqrt(2 * m * E)
p = sqrt(2 * 1.67 x 10^-27 kg * 1.6 x 10^-13 J)
p ≈ 137.4 MeV/c
Therefore, the correct option is: 10.5 MeV/c, 137.4 MeV/c.
To find the relativistic momentum of a particle accelerated through a potential, we need to use the relativistic equation:
p = sqrt[(E^2) - (m^2c^4)] / c
where:
p is the relativistic momentum,
E is the total energy of the particle (kinetic energy + rest energy),
m is the mass of the particle, and
c is the speed of light.
In this case, we are given the potential difference of 10*10^6 volts.
The total energy of a particle can be calculated using the equation:
E = mc^2 + qV
where:
q is the charge of the particle, and
V is the potential difference.
For an electron, q is equal to the elementary charge, e. The rest mass of an electron is approximately 9.11 * 10^-31 kg.
So, the total energy of an electron accelerated through a potential of 10*10^6 volts would be:
E_electron = (9.11 * 10^-31 kg) * (3 * 10^8 m/s)^2 + (1.6 * 10^-19 C) * (10 * 10^6 V)
E_electron = 1.64 * 10^-14 J
Next, let's calculate the relativistic momentum of the electron:
p_electron = sqrt[(E_electron^2) - (m_electron^2c^4)] / c
Using the values given, we can calculate:
p_electron ≈ 10.5 MeV/c
For a proton, the charge is equal to the elementary charge, e, and the rest mass is approximately 1.67 * 10^-27 kg.
So, the total energy of a proton accelerated through a potential of 10*10^6 volts would be:
E_proton = (1.67 * 10^-27 kg) * (3 * 10^8 m/s)^2 + (1.6 * 10^-19 C) * (10 * 10^6 V)
E_proton ≈ 2.82 * 10^-13 J
Next, let's calculate the relativistic momentum of the proton:
p_proton = sqrt[(E_proton^2) - (m_proton^2c^4)] / c
Using the values given, we can calculate:
p_proton ≈ 137.4 MeV/c
Therefore, the correct answer is 10.5 MeV/c , 137.4 MeV/c.