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Chapter 3: 8CQ (page 92)

A ball rebounds elastically from the floor. What doesthis situation share with the ideas of momentum conservation discussed in connection with pair production?

Short Answer

Expert verified

In pair production, the higher mass nucleus alters the momentum of the incoming photon significantly during the collision but absorbs negligible kinetic energies during the collision. Hence, the laws of energy and momentum conservations hold.

Step by step solution

01

Concept used

Pair production is a phenomenon in which a photon of sufficiently high energy interacting with a matter forms an electron and positron in the vicinity of a nucleus. The laws of energy and momentum conservations hold only in the vicinity of the nucleus.

02

Energy conservation

When a ball hits the floor and rebounds back elastically,,there is a negligible loss of kinetic energy of the ball. So, the initial kinetic energy of the ball is the same as the final kinetic energy. The momentum of the floor upon collision is comparable to the momentum of the falling ball. But, the kinetic energy transferred by the ball to the floor is negligible due to a huge difference in the mass of the ball and the floor. Hence, the laws of energy conservation and momentum conservation hold.

03

Conservation of momentum

Now, when a photon having very high energy interacts with the matter, an electron and a positron are produced with equal momentum and kinetic energies. The nucleus behaving like the floor absorbs negligible kinetic energy from the incoming photon, which acts like the falling ball. So, the initial energy of the photon is equal to the combined energies of the electron and positron. Also, the higher mass nucleus significantly alters the momentum of the photon and thus, momentum is also conserved.

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Most popular questions from this chapter

From equations (3-4) to (3-6) obtain equations (3.8). It is easiest to start by eliminating 蠁 between equations (3-4) and (3-5) using cos2蠁+蝉颈苍2蠁 = 1 The electron speed u may then be eliminated between the remaining equations.

In the Compton effect, we choose the electron to be at the origin and the initial photon's direction of motion to be in the+x-direction.

(a) We may also choose the xy-plane so that it contains the velocities of the outgoing electron and photon. Why? (b) The incoming photon's wavelength位is assumed to be known. The unknowns after the collision are the outgoing photon's wavelength and direction,位鈥�, and 胃,and the speed and direction of theelectron,ue,and蠒.With only three equationstwocomponents of momentum conservation and one of energy, we can't find all four. Equation(3鈭�8)gives位鈥瞚n terms of胃.Our lack of knowledge of 胃胃 after the collision (without an experiment) is directly related to a lack of knowledge of something before the collision. What is it? (imagine the two objects are hard spheres.) (c) Is it reasonable to suppose that we could know this? Explain.

What is the wavelength of a 2.0mWIaser from which "6脳1015 photons emanate every second?

A bedrock topic in quantum mechanics is the uncertainty principle. It is discussed mostly for massive objects in Chapter 4, but the idea also applies to light: Increasing certainty in knowledge of photon position implies increasing uncertainty in knowledge of its momentum, and vice versa. A single-slit pattern that is developed (like the double-slit pattern of Section 3.6) one photon at a time provides a good example. Depicted in the accompanying figure, the pattern shows that pho tons emerging from a narrow slit are spreadall-over; a photon's x-component of momentum can be any value over a broad range and is thus uncertain. On the other hand, the x -coordinate of position of an emerging photon covers a fairly small range, for w is small. Using the single-slit diffractionformula 苍位=飞蝉颈苍胃 , show that the range of likely values of px, which is roughly 辫蝉颈苍胃 , is inversely proportional to the range w of likely position values. Thus, an inherent wave nature implies that the precisions with which the particle properties of position and momentum can be known are inversely proportional.

Light of wave length590nm is barely able to eject electrons from a metal plate. What would be the speed of the fastest electrons ejected by the light of one-third the wavelength?
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