To find the relativistic momentum of protons accelerated to a kinetic energy of 470 MeV in a linear accelerator, we can use the formula p = √(2mE), where p is the momentum, m is the rest mass of the proton, and E is the kinetic energy. By substituting the given values into the formula, the relativistic momentum is found to be 6.82 x 10⁻¹⁹ kg m/s.
To find the relativistic momentum of protons accelerated to a kinetic energy of 470 MeV in a linear accelerator, we can use the formula:
p = √(2mE)
where p is the momentum, m is the rest mass of the proton (1.67 x 10⁻²⁷ kg), and E is the kinetic energy (470 MeV).
First, convert the kinetic energy to joules by multiplying it by the conversion factor:
1 MeV = 1.6 x 10⁻¹³ J
So, 470 MeV = 470 x 1.6 x 10⁻¹³ J = 7.52 x 10⁻¹¹ J
Now, substitute the values into the formula:
p = √(2 x 1.67 x 10⁻²⁷ kg x 7.52 x 10⁻¹¹ J)
Calculating the expression gives:
p = 6.82 x 10⁻¹⁹ kg m/s
Therefore, the relativistic momentum of the protons is 6.82 x 10⁻¹⁹ kg m/s.