K* Meson: Rest Mass to Relativistic Momentum

[FateEternal]

The excited K* meson has a rest mass of 1.5828E-27 kg/
a What is the rest amss energy in joules?
1.43E-10
b What is this energy in MeVs?
893.75
here's where i need help
c Now these K* are accelerated to a speed of 2.97E8 m/sec. What is the relatavistic mass of these K* in kg and MeV/c squared
so far i have 1.5828E-27/radical(1-.99csquared)=1.12E-26
do I convert into MeV's and divide by 3E8squared?
so 6282/3E8squared
=6.98E-14 MeV/c squared
d What is the relatavistic momentum of these K* in kgm/sec and in MeV/c?

 

[Jhero]

To find the relativistic mass, you would use the formula: m = m0/√(1-v^2/c^2), where m0 is the rest mass, v is the velocity, and c is the speed of light. In this case, m0 = 1.5828E-27 kg and v = 2.97E8 m/s. Plugging in these values, we get m = 1.5828E-27/√(1-(2.97E8)^2/(3E8)^2) = 1.5828E-27/√(1-0.99) = 1.5828E-27/0.1414 = 1.1206E-26 kg. This is the relativistic mass of the K* in kg.

To convert this into MeV/c^2, we can use the conversion factor 1 kg = 8.99E16 MeV/c^2. So the relativistic mass in MeV/c^2 would be 1.1206E-26 kg * 8.99E16 MeV/c^2 = 1.0068E-9 MeV/c^2.

To find the relativistic momentum, we can use the formula: p = mv, where m is the relativistic mass we just calculated and v is the velocity. So the relativistic momentum would be p = 1.1206E-26 kg * 2.97E8 m/s = 3.3321E-18 kgm/s. In terms of MeV/c, this would be 3.3321E-18 kgm/s * (3E8)^2/8.99E16 MeV/c^2 = 1.1109E-9 MeV/c.