Question

The mass ofZo is 9.1X100 eve a) Calculate how long a virtual Z can last according to the HUP 1) b) Calculate how far the Z can go in this time, even if it were traveling at the speed of light. The answer to (b) is approximately the range of the weak force. Are electrons in different atoms close enough to interact by the weak force? (Atomic spacing is generally a few Angstroms) c) 2) Which of the four fundamental forces is each of the following particles affected by? a) electrorn b) proton c) neutrino

Answer 1

Mass Z degree = 9.1 times 10^10 e Y/C^2 a) (Ignoring Relavistic Properties) We can write E = mc^2 E_Z degree = 9.1 times 10^10 [eV/C^2] times C^2 E = 9.1 times 10^10 HUP energy time relative gives us Delta E middot Delta t greaterthanorequalto h/4 pi Rightdoublearrow Delta t = h/4 pi times Delta E Delta t = h/4 pi times 9.1 times 10^10 = 6.63 times 10^- 34 [J.S]/4 times pi times 9.1 times 10^10 times 1.6 times 10^- 19 [J] to convert ev rightarrow J) Therefore Delta t = 3.625 times 10^- 24 S b) At V = C [count use S.T.R Because r = 00 rightarrow t = rt_0 Rightdoublearrow dialated time = infinity] V = d/t Rightdoublearrow d = v times t = c times 3.625 times 10^- 27 = 3 times 10^8 times 3.625 times 10^- 27 = 1.087 times 10^- 18 m = 1.087 times 10^- 8 A^o c) Range of weak force is about 10^- 18 m. 1A^o =