Question

Rutherford's scattering experiments gave the first indications that an atom consists of a small, dense, positively charged nucleus surrounded by negatively charged electrons. His experiments also allowed for a rough determination of the size of the nucleus. In this problem, you will use the uncertainty principle to get a rough idea of the kinetic energy of a particle inside the nucleus.

Consider a nucleus with a diameter of roughly 5.0×10−15 meters.

The uncertainty Δp sets a lower bound on the average momentum of a particle in the nucleus. If a particle's average momentum were to fall below that point, then the uncertainty principle would be violated. Since the uncertainty principle is a fundamental law of physics, this cannot happen. Using Δp=1.06×10−20 kilogram-meters per second as the minimum momentum of a particle in the nucleus, find the minimum kinetic energy Kmin of the particle. Use m=1.67×10−27 kilograms as the mass of the particle. Note that since our calculations are so rough, this serves as the mass of a neutron or a proton.

K(min)= (Answer) MeV

Answer 1

Dear , please find the answer slide given below for your reference.

2 Thousand 19 FRIDAY MAY DAY 151 214 WEEK 22 I 1000 Given nucleus with diametu = 5x10 metres. AP = 1,00 x10 20 lg.ee man = 1.07x10-27 lg (kz)=2 all know uncertainity in particle momentum is An AP > h20 (where h- planck A) We 1200 Now, all we know is 3.00 6.00 TAP = momx velocity 100X1020 = 1.62x10 ** x velocity velocity = 6347, 305 xto 3 m/sec K. E- / mv² = ',x1.67X10** *x76347,305 X103)2 IKE = 3.36 407 x 10 J WTFS MTWTFS M T WISS MI W T F S S M T W T F S S JUN 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 2019 Courage is like love; it must have hope for nourishment