Answer:
Use the principle of momentum
Initial momentum = final momentum
Momentum formula = Mass * Velocity
Explanation:
Answer:
![KE=1.2036\times 10^{-12}\ J](https://tex.z-dn.net/?f=KE%3D1.2036%5Ctimes%2010%5E%7B-12%7D%5C%20J)
Explanation:
Given:
- charge on the alpha particle,
![q=2e=3.2\times 10^{-19}\ C](https://tex.z-dn.net/?f=q%3D2e%3D3.2%5Ctimes%2010%5E%7B-19%7D%5C%20C)
- mass of the alpha particle,
![m=6.64\times 10^{-27}\ kg](https://tex.z-dn.net/?f=m%3D6.64%5Ctimes%2010%5E%7B-27%7D%5C%20kg)
- strength of a uniform magnetic field,
![B=0.5\ T](https://tex.z-dn.net/?f=B%3D0.5%5C%20T)
- radius of the final orbit,
![r=0.5\ m](https://tex.z-dn.net/?f=r%3D0.5%5C%20m)
<u>During the motion of a charge the magnetic force and the centripetal forces are balanced:</u>
![q.v.B=m.\frac{v^2}{r}](https://tex.z-dn.net/?f=q.v.B%3Dm.%5Cfrac%7Bv%5E2%7D%7Br%7D)
![m.v=q.B.r](https://tex.z-dn.net/?f=m.v%3Dq.B.r)
where:
v = velocity of the alpha particle
![v=\frac{q.B.r}{m}](https://tex.z-dn.net/?f=v%3D%5Cfrac%7Bq.B.r%7D%7Bm%7D)
![v=\frac{3.2\times 10^{-19}\times 0.5\times 0.5}{6.64\times 10^{-27}}](https://tex.z-dn.net/?f=v%3D%5Cfrac%7B3.2%5Ctimes%2010%5E%7B-19%7D%5Ctimes%200.5%5Ctimes%200.5%7D%7B6.64%5Ctimes%2010%5E%7B-27%7D%7D)
![v=1.2048\times 10^{7}\ m.s^{-1}](https://tex.z-dn.net/?f=v%3D1.2048%5Ctimes%2010%5E%7B7%7D%5C%20m.s%5E%7B-1%7D)
Here we observe that the velocity of the aprticle is close to the velocity of light. So the kinetic energy will be relativistic.
<u>We firstly find the relativistic mass as:</u>
![m'=\frac{1}{\sqrt{1-\frac{v^2}{c^2} } } \times m](https://tex.z-dn.net/?f=m%27%3D%5Cfrac%7B1%7D%7B%5Csqrt%7B1-%5Cfrac%7Bv%5E2%7D%7Bc%5E2%7D%20%7D%20%7D%20%5Ctimes%20m)
![m'=\frac{6.64\times 10^{-27}}{\sqrt{1-\frac{(1.2048\times 10^7)^2}{(3\times 10^8)^2} } }](https://tex.z-dn.net/?f=m%27%3D%5Cfrac%7B6.64%5Ctimes%2010%5E%7B-27%7D%7D%7B%5Csqrt%7B1-%5Cfrac%7B%281.2048%5Ctimes%2010%5E7%29%5E2%7D%7B%283%5Ctimes%2010%5E8%29%5E2%7D%20%7D%20%7D)
![m'=6.6533\times10^{-27}\ kg](https://tex.z-dn.net/?f=m%27%3D6.6533%5Ctimes10%5E%7B-27%7D%5C%20kg)
now kinetic energy:
![KE=m'.c-m.c](https://tex.z-dn.net/?f=KE%3Dm%27.c-m.c)
![KE=6.6533\times 10^{-27}\times (3\times 10^8)^2-6.64\times 10^{-27}\times (3\times 10^8)^2](https://tex.z-dn.net/?f=KE%3D6.6533%5Ctimes%2010%5E%7B-27%7D%5Ctimes%20%283%5Ctimes%2010%5E8%29%5E2-6.64%5Ctimes%2010%5E%7B-27%7D%5Ctimes%20%283%5Ctimes%2010%5E8%29%5E2)
![KE=1.2036\times 10^{-12}\ J](https://tex.z-dn.net/?f=KE%3D1.2036%5Ctimes%2010%5E%7B-12%7D%5C%20J)
Answer:
1, 2, 3, and 6 are the answers.
Explanation:
sorry for the late response
E = MC^2. Albert Einstein's proven formula. When mass travels at the square of speed of light, the mass gets converted into energy
Hi,
The correct answer is C. five
I hope I helped :)