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Chapter 38: Q. 17 (page 1114)

17. What is the de Broglie wavelength of a neutron that has fallen 1.0min a vacuum chamber, starting from rest?

Short Answer

Expert verified

The de Broglie wavelength of the neutron that has fallen 1.0min a vacuum chamber isλ=90nm

Step by step solution

01

Given information 

the de Broglie wavelength of a neutron that has fallen 1.0min a vacuum chamber,

02

calculation 

The neutron has traveled through the gravitational potential energy difference of

E=mgΔy

where Δy=1.0m. This potential energy difference is converted into neutron's kinetic energy, so

T=mgΔy

We also know that the kinetic energy is related to momentum through

T=p22m

Therefore

p22m=mgΔy

yielding

p=m2gΔy.

De Broglie wavelength is then simply given by

+λ-hp=hm2gΔy.

Remember that h=6.626·10-34Js, and that the mass of the neutron is m=1.67·10-27kg. With these numerical values we get

λ=90nm

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Most popular questions from this chapter

The first three energy levels of the fictitious element X are shown in Figure.

a. What is the ionization energy of element X?

b. What wavelengths are observed in the absorption spectrum of element X? Express your answers in nm.

c. State whether each of your wavelengths in part b corresponds to ultraviolet, visible, or infrared light.

The cosmic microwave background radiation is light left over from the Big Bang that has been Doppler-shifted to microwave frequencies by the expansion of the universe. It now fills the universe with 450 photons/cm3 at an average frequency of 160 GHz. How much energy from the cosmic microwave background, in MeV, fills a small apartment that has 95 m2 of floor space and 2.5-m-high ceilings?

I FIGURE EX38.24 is an energy-level diagram for a simple atom. What wavelengths, in \mathrm{nm}, appear in the atom's (a) emission spectrum and (b) absorption spectrum?

n=3⟶E3=4.00eV

n=2-E2=1.50eV

FIGURE EX38.24 n=1-E_{1}=0.00 \mathrm{eV}

The maximum kinetic energy of photoelectrons is 2.8 eV. When the wavelength of the light is increased by 50%, the maximum energy decreases to 1.1 eV. What are (a) the work function of the cathode and (b) the initial wavelength of the light?

How would the graph of Figure 38.2 look if classical physics provided the correct description of the photoelectric effect? Draw the graph and explain your reasoning. Assume that the light intensity remains constant as its frequency and wavelength are varied.
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