Show (by calculating the velocity in terms of c ) that ifan electron were confin
ID: 1679883 • Letter: S
Question
Show (by calculating the velocity in terms of c) that ifan electron were confined inside an atomic nucleus of diameter2.2 x 10-15 m, itwould have to be moving relativistically, whereas a proton confinedto the same nucleus can be moving at less than one-tenth the speedof light. (Give all answers to 4 decimal places.) (a) When the confined particle is an electron,ER = 0.511 MeV.1_________c
(b) When the confined particle is a proton, ER= 939 MeV.
2_________c (a) When the confined particle is an electron,ER = 0.511 MeV.
1_________c
(b) When the confined particle is a proton, ER= 939 MeV.
2_________c
Explanation / Answer
the change in momentum is given by p > or = h / 4 (x) = [(6.63 x 10-34 J . s) / 4 (2.0 x10-15 m)] (1 MeV / 1.60 x 10-19 J) = ............ MeV . s / m here since the momentum must be at leastas large as its own uncertainty we get p >= ............ MeV . s / m (a) if the confined particle is an electron then ER = 0.511 MeV E = [(p c)2 +ER2] = E / ER so the speed will be v = c [1 - (1 / 2)] = ......... c (b) if the confined particle is a proton thenER = 939 MeV E = [(p c)2 +ER2] = E / ER so the speed will be v = c [1 - (1 / 2)] = ......... c