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Chapter 38: Q13Q (page 1181)

The following nonrelativistic particles all have the same kinetic energy. Rank them in order of their de Broglie wavelengths, greatest first: electron, alpha particle, neutron.

Short Answer

Expert verified

The rank is electron, neutron, alpha particle.

Step by step solution

01

Describe the de Broglie wavelength

The de Broglie wavelength is given by,

λ=hmv

Here, h is the plank’s constant, m is the mass and v is the velocity.

02

Rank the de Broglie wavelengths for electron, alpha particle, and neutron

From the de Broglie wavelength, it can be observed that the mass of the particle is inversely proportional to the wavelength.

It is known that the mass of the neutron is mn=1.67×10-27kg, the mass of alpha particle is mα=6.664×10-27kg and the mass of the electron is me=9.11×10-31kg.Clearly, me<mn<mα. So, rank of de Broglie wavelength is λe>λn>λα.

Therefore, the rank is electron, neutron, alpha particle.

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Most popular questions from this chapter

Question: You will find in Chapter 39 that electrons cannot move in definite orbits within atoms, like the planets in our solar system. To see why, let us try to “observe” such an orbiting electron by using a light microscope to measure the electron’s presumed orbital position with a precision of, say, 10pm(a typical atom has a radius of about localid="1663132292844" 100pm). The wavelength of the light used in the microscope must then be about 10pm. (a) What would be the photon energy of this light? (b) How much energy would such a photon impart to an electron in a head-on collision? (c) What do these results tell you about the possibility of “viewing” an atomic electron at two or more points along its presumed orbital path? (Hint:The outer electrons of atomsare bound to the atom by energies of only a few electron-volts.)

Through what angle must a200 keVphoton be scattered by a free electron so that the photon loses 10%of its energy?

A nonrelativistic particle is moving three times as fast as an electron. The ratio of the de Broglie wavelength of the particle to that of the electron is 1.813×10−4. By calculating its mass, identify the particle.

Question: For the arrangement of Figs. 38-14 and 38-15 , electrons in the incident beam in region 1 have energy E=800eV and the potential step has a height of U1=600eV. What is the angular wave number in (a) region 1 and (b) region 2 ? (c) What is the reflection coefficient? (d) If the incident beam sends 500×105electrons against the potential step, approximately how many will be reflected?

Fig 38-14

Fig 38-15

In a Compton-shift experiment, light (in the x-ray range) is scattered in the forward direction, atϕ=0 in Fig. 38-3. What fraction of the light’s energy does the electron acquire?
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