What is the distance between the points (1, –2, 5) and (-1,3, 2) ? O V78 O V14 O VIO O V34

Why don't we notice quantization in everyday events?

Prove that, to three-digit accuracy, h=4.141015eVs, as stated in the text.

Check Your Understanding What is if v=0.650c?

(a) Calculate the mass of a proton using the charge-to-mass ratio given for it in this chapter and its known charge. (b) How does your result compare with the proton mass given in this chapter?

Cosmic rays are high-energy charged particles produced by astronomical objects. Many of the cosmic rays that make their way to the Earth are trapped by the Earths magnetic field and never reach the surface. These trapped cosmic rays are found in the Van Allen beltsdonut-shaped zones over the Earths equator (Fig. 30.34). These cosmic rays are mostly protons with energies of about 30 MeV. The inset in the figure shows a cosmic ray proton as it is about to enter the Earths magnetic field. The cosmic rays velocity is initially perpendicular to the field. Three students discuss what happens to the incoming cosmic ray. Decide which student or students are correct. Figure 30.34 The Van Allen belts are donut-shaped zones of trapped cosmic rays above the Earths surface. Inset: What happens to this cosmic ray as it enters the Earths magnetic field? Shannon: The velocity is perpendicular to the magnetic field, so the cosmic ray just passes through the field and hits the Earths atmosphere. Avi: What you are saying is that the magnetic field exerts no force on the cosmic ray. Actually, it exerts a huge force because the velocity is perpendicular to the magnetic field. The force will be into the page. Cameron: Avi is right. The cosmic ray proton is going to feel a huge magnetic force. Because it is positively charged, it will be pushed upward along the magnetic field lines. Shannon: I never said the force was zero. There is a force, but the force is perpendicular to the magnetic field lines. In this case, thats to the lefttoward the Earth. Avi: The force is perpendicular to the magnetic field, but it also has to be perpendicular to the velocity. Because B and v are both in the plane of the page, the force must be perpendicular to the page.

The velocity of a proton emerging from a Van de Graaff accelerator is 25.0% of the speed of light. (a) What is the proton's wavelength? (b) What is its kinetic energy, assuming it is nonrelativistic? (c) What was the equivalent voltage through which it was accelerated?

An observer in a coasting spacecraft moves toward a mirror at speed v relative to the reference frame labeled by S in Figure P26.46. The mirror is stationary with respect to S. A light pulse emitted by the spacecraft travels toward the mirror and is reflected back to the spacecraft. The spacecraft is a distance d from the mirror (as measured by observers in S) at the moment the light pulse leaves the spacecraft. What is the total travel time of the pulse as measured by observers in (a) the S frame and (b) the spacecraft? Figure P26.46

List all the possible values of s and msfor an electron. Are there particles for which these values are different? The same?

(a) If the position of an electron in a membrane is measured to an accuracy of 1.00 m, what is the electron's minimum uncertainty in velocity? (b) If the electron has this velocity, what is its kinetic energy in eV? (c) What are the implications of this energy, comparing it to typical molecular binding energies?