The momentum of a proton would be:
(a) For particle moving with speed 0.010c
p = 5.016 × 10^(-21) kgms^{-1}
p = 9.398 MeV/c
(b) For particle moving with speed 0.50c
p = 2.89 × 10^(-19) kgms^{-1}
p = 541.5 MeV/c
(c) For particle moving with speed 0.90c
p = 23.73 × 10^(-19) kgms^{-1}
p = 4446.35 MeV/c
For given question,
We need to calculate the momentum of a proton moving with a given speed.
We know that, the equation for relativistic momentum is,
![p=\frac{mv}{\sqrt{1-\frac{v^2}{c^2} } }](https://tex.z-dn.net/?f=p%3D%5Cfrac%7Bmv%7D%7B%5Csqrt%7B1-%5Cfrac%7Bv%5E2%7D%7Bc%5E2%7D%20%7D%20%7D)
We know, the mass of proton (m) =
kg
(a) For particle moving with speed 0.010c
v = 0.010c
the momentum of a proton would be,
![\Rightarrow p=\frac{(1.67\times 10^{-27}kg)\times (0.010\times 3\times 10^8)\frac{m}{s} }{\sqrt{1-\frac{0.01^2~c^2}{1^2~c^2} } }\\\\\Rightarrow p=5.016\times 10^{-21}~~kgms^{-1}](https://tex.z-dn.net/?f=%5CRightarrow%20p%3D%5Cfrac%7B%281.67%5Ctimes%2010%5E%7B-27%7Dkg%29%5Ctimes%20%280.010%5Ctimes%203%5Ctimes%2010%5E8%29%5Cfrac%7Bm%7D%7Bs%7D%20%7D%7B%5Csqrt%7B1-%5Cfrac%7B0.01%5E2~c%5E2%7D%7B1%5E2~c%5E2%7D%20%7D%20%7D%5C%5C%5C%5C%5CRightarrow%20p%3D5.016%5Ctimes%2010%5E%7B-21%7D~~kgms%5E%7B-1%7D)
(b) For particle moving with speed 0.50c
v = 0.50c
the momentum of a proton would be,
![\Rightarrow p=\frac{(1.67\times 10^{-27}kg)\times (0.50\times 3\times 10^8)\frac{m}{s} }{\sqrt{1-\frac{0.5^2~c^2}{1^2~c^2} } }\\\\\Rightarrow p=2.89\times 10^{-19}~~kgms^{-1}](https://tex.z-dn.net/?f=%5CRightarrow%20p%3D%5Cfrac%7B%281.67%5Ctimes%2010%5E%7B-27%7Dkg%29%5Ctimes%20%280.50%5Ctimes%203%5Ctimes%2010%5E8%29%5Cfrac%7Bm%7D%7Bs%7D%20%7D%7B%5Csqrt%7B1-%5Cfrac%7B0.5%5E2~c%5E2%7D%7B1%5E2~c%5E2%7D%20%7D%20%7D%5C%5C%5C%5C%5CRightarrow%20p%3D2.89%5Ctimes%2010%5E%7B-19%7D~~kgms%5E%7B-1%7D)
(c) For particle moving with speed 0.90c
v = 0.90c
the momentum of a proton would be,
![\Rightarrow p=\frac{(1.67\times 10^{-27}kg)\times (0.90\times 3\times 10^8)\frac{m}{s} }{\sqrt{1-\frac{0.90^2~c^2}{1^2~c^2} } }\\\\\Rightarrow p=23.73\times 10^{-19}~~kgms^{-1}](https://tex.z-dn.net/?f=%5CRightarrow%20p%3D%5Cfrac%7B%281.67%5Ctimes%2010%5E%7B-27%7Dkg%29%5Ctimes%20%280.90%5Ctimes%203%5Ctimes%2010%5E8%29%5Cfrac%7Bm%7D%7Bs%7D%20%7D%7B%5Csqrt%7B1-%5Cfrac%7B0.90%5E2~c%5E2%7D%7B1%5E2~c%5E2%7D%20%7D%20%7D%5C%5C%5C%5C%5CRightarrow%20p%3D23.73%5Ctimes%2010%5E%7B-19%7D~~kgms%5E%7B-1%7D)
Now, we need to convert answers into MeV/c
1 MeV = 1.6 × 10^(-13) kg.m²/s²
⇒ 1 kg.m²/s² = 625 × 10^(10) MeV
1 c = 299,792,458 m/s
⇒ 1 m/s = 3.3356E-9 c
So, 1 kg. m/s = 1.8737259e+21 MeV/c
(a) For p = 5.016 × 10^(-21) kgms^{-1}
⇒ p = 5.016 × 10^(-21) × 1.8737259e+21
⇒ p = 9.398 MeV/c
(b) For p = 2.89 × 10^(-19) kgms^{-1}
⇒ p = 2.89 × 10^(-19) × 1.8737259e+21
⇒ p = 541.5 MeV/c
(c) For p = 23.73 × 10^(-19) kgms^{-1}
⇒ p = 23.73 × 10^(-19) × 1.8737259e+21
⇒ p = 4446.35 MeV/c
Therefore, the momentum of a proton would be:
(a) For particle moving with speed 0.010c
p = 5.016 × 10^(-21) kgms^{-1}
p = 9.398 MeV/c
(b) For particle moving with speed 0.50c
p = 2.89 × 10^(-19) kgms^{-1}
p = 541.5 MeV/c
(c) For particle moving with speed 0.90c
p = 23.73 × 10^(-19) kgms^{-1}
p = 4446.35 MeV/c
Learn more about the momentum here:
brainly.com/question/12942930
#SPJ4