UNIVERSITY OF TORONTO

Midterm Test

PHY 357S

Duration - 50 Minutes

Allowed aids: Calculator and 1 letter-sized double-sided hand-written aid sheet.

Do 3 of 4 questions; each question has equal weight.

If you do all 4 questions, your best 3 marks will be used.

Each part of a multipart question is of equal weight.

Show your work and reasoning; part marks will be given.

Useful information is given on the last two pages of this exam.

* Some of the following numerical constants may be useful:

 pi p= 3.14159265358979323… speed of light c = 299792458 m s-1 Planck's constant, reduced h/2p = 6.58212x10-22 MeV s conversion constants hc/2p = 197.327 MeV fm (hc/2p)2 = .389379 GeV2 mb conversion factors 1 eV = 1.602177x10-19 J 1 eV/c2 = 1.782662x10-36 kg 1 barn = 10-24 cm2 unified atomic mass unit u = 931.494 MeV/c2 Avogadro's constant NA = 6.022137x1023 mol-1 electron charge e = 1.602x10-19 C electron magnetic moment µe = 2.9665x10-7 eV-1 Boltzmann constant k = 8.617x10-5 eV/Kelvin fine structure constant a= 1/137.0360 strong coupling constant aS(MZ)= 0.118±0.003 Cabibbo angle sin qc @ Vus = 0.22 weak mixing angle sin2qW= 0.2315 standard grav. accel., sea level g = 9.8 m/s2 Hubble constant H0=0.1 Gyr-1 neutral kaon mass difference mKL- mKS = 3.510±0.018 meV Fermi weak coupling constant GF = 1.166x10-5 GeV-2 Newton's (gravitational) constant GN = 6.673x10-11m3kg-1s-2 = 6.707x10-39 GeV-2 Z0 branching fractions B.R.(Z0->e+e-)=3.21±0.07% B.R.(Z0->hadrons) = 71±1%

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* Particle Properties *

 Boson Mass (GeV/c2) Lepton Mass (MeV/c2) Mean Lifetime Quarks mass (GeV/c2) g <3¥10-36 ne <10-5 u ~0.005 gluon <0.01 e- 0.510999 >4.3¥1023 y d ~0.01 W± 80.22 nµ <0.27 c 1.0-1.5 Z0 91.187 µ- 105.658 2.197 µs s 0.1-0.3 H0 >58 nt <10 t 174±6 graviton ~0 t- 1777 0.29 ps b ~4.5

 Hadron Quark Content Mass (MeV/c2) I(JPC) p0 (u-d)/21/2 134.97 1(0-+) p+, p- u, d 139.57 1(0-) K+,K- u, s 493.65 K0, anti-K0 d, s 497.67 r+, r0, r- u, (u-d)/21/2, d 770 1(1--) p uud 938.27 n udd 939.57 L uds 1115.6 0(1/2+) S0 uds 1192.6 1(1/2+) D-, D0, D+, D++ ddd, udd, uud, uuu 1232 3/2 (3/2+) D0, anti-D0 u, c 1863 1/2 (0-) D+,D- d, c 1869 1/2 (0-) Lc udc 2285 0(1/2-) B+,B- u, b 5279 1/2 (0-) Lb udb 5640±50 0(1/2+)

 Nuclei Mass (in u) Nuclei Mass (in u) Nuclei Mass (in u) H1 1.007825 2He3 3.01603 26Fe56 55.934939 1H2 2.0140 2He4 4.00260 82Pb208 207.976627 1H3 3.01605 6C12 12

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Problem 1

(a) An electron accelerator is to be designed to study properties of linear dimensions of 1 fm. What kinetic energy is required?

(b) What is the magnetic moment of a hydrogen atom?

Problem 2

This is a sketch of a very rare two-body decay of a neutral particle.

The sketch has been reduced and a scale provided.The two particle tracks shown lie in the plane of the paper; the initial angle between the two tracks at the decay point is 90°. There is a magnetic field of 3.33 Tesla (33,333 Gauss) perpendicular to the page. What is the mass of the unknown particle? (You don't need to calculate the uncertainty in the mass.)

Problem 3

Explain how Rutherford's alpha-gold scattering data showed that the electric charge in atoms is not uniformly distributed over the entire volume of the atom.

### Problem 4

A isospin I=1 meson is observed to decay into 3 pions but not into 2 pions. (a) Is the weak interaction responsible for this decay? (b) What is the strangeness of the charged meson?

This is the last page of this test.