Problems are listed in approximate order of difficulty. A single dot (•) indicates straigh...

Problems are listed in approximate order of difficulty. A single dot (•) indicates straightforward problems involving just one main concept and sometimes requiring no more than substitution of numbers in the appropriate formula. Two dots (••) identify problems that are slightly more challenging and usually involve more than one concept. Three dots (•••) indicate problems that are distinctly more challenging, either because they are intrinsically difficult or involve lengthy calculations. Needless to say, these distinctions are hard to draw and are only approximate.

••• Figure 1 shows the track of a K+ meson in a bubble chamber. The K+ has decayed into a μ+ and an invisible neutrino: K+ → μ+ + vμ. The paths of the charged particles were curved by a magnetic field B = 0.50 T directed out of the page. The measured radii of the curved paths are RK = 1.0 m for the K+ and Rμ = 1.7 m for the μ+. (a) Use this information to find the momenta of the K+ and μ+. [Recall Eq. (2.48), relating R to p.] (b) The angle between pK and pμ at the moment of decay is 71°, as shown. Deduce the momentum of the invisible neutrino. (c) Assuming the known masses of the μ+ and vμ (mμ = 106 MeV/c2 and mv ≈ 0), calculate their energies. (d) Deduce the energy of the K+, and hence find its mass and speed.

FIGURE 1