Chapter 38: Photons and Matter Waves

Question: For the arrangement of Figs. $\mathbf{38}\mathbf{-}\mathbf{14}$ and $\mathbf{38}\mathbf{-}\mathbf{15}$ , electrons in the incident beam in region 1 have energy $\mathbf{E}\mathbf{=}\mathbf{800}\mathbf{}\mathbf{eV}$ and the potential step has a height of ${\mathbf{U}}_{\mathbf{1}}\mathbf{=}\mathbf{600}\mathbf{}\mathbf{eV}$. 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 $\mathbf{500}\mathbf{\times }{\mathbf{10}}^{\mathbf{5}}$electrons against the potential step, approximately how many will be reflected?

Fig 38-14

Fig 38-15

Question:For the arrangement of Figs. 38-14 and 38-15, electrons in the incident beam in region 1 have a speed of $\mathbf{1}\mathbf{.}\mathbf{60}\mathbf{\times }{\mathbf{10}}^{\mathbf{7}}\mathbf{}\mathbf{m}\mathbf{/}\mathbf{s}$and region 2 has an electric potential of ${\mathit{V}}_{\mathbf{2}}\mathbf{-}\mathbf{500}\mathbf{}\mathit{V}$. 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 $\mathbf{3}\mathbf{.}\mathbf{00}\mathbf{\times }{\mathbf{10}}^{\mathbf{9}}$electrons against the potential step, approximately how many will be reflected?

Fig 38-14

Fig 38-15

Question: The current of a beam of electrons, each with a speed of $\mathbf{900}\mathbf{}\mathbf{m}\mathbf{/}\mathbf{s}$, is $\mathbf{5}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{A}$. At one point along its path, the beam encounters

a potential step of height $\mathbf{-}\mathbf{1}\mathbf{.}\mathbf{25}\mathbf{}\mathbf{\mu V}$.What is the current on the other side of the step boundary?

Question:Consider a potential energy barrier like that of Fig. 38-17but whose height ${\mathbf{U}}_{\mathbf{b}}$is and $\mathbf{6}\mathbf{}\mathbf{eV}$whose thickness Lis $\mathbf{0}\mathbf{.}\mathbf{70}\mathbf{}\mathbf{nm}$. What is the energy of an incident electron whose transmissioncoefficient is $\mathbf{0}\mathbf{.}\mathbf{0010}$?

Question:A $\mathbf{0}\mathbf{.}\mathbf{30}\mathbf{}\mathbf{MeV}$proton is incident on a potential energy barrier of thickness $\mathbf{10}\mathbf{}\mathbf{fm}$and height $\mathbf{10}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{MeV}$.What are (a) the transmission coefficient T , (b) the kinetic energy ${\mathbf{K}}_{\mathbf{t}}$ the proton will have on the other side of the barrier if it tunnels through the barrier, and (c) the kinetic energy ${\mathbf{K}}_{\mathbf{r}}$ it will have if it reflects from the barrier? A $\mathbf{3}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{MeV}$ deuteron (the same charge but twice the mass as a proton) is incident on the same barrier. What are (d) T , (e) ${\mathbf{K}}_{\mathbf{t}}$, and (f) ${\mathbf{K}}_{\mathbf{r}}$?

Question: (a) Suppose a beam of $\mathbf{5}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{eV}$ protons strikes a potential energy barrier of height $\mathbf{6}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{eV}$and thickness $\mathbf{0}\mathbf{.}\mathbf{70}\mathbf{}\mathbf{nm}$, at a rate equivalent to a current of $\mathbf{1000}\mathbf{}\mathbf{A}$. How long would you have to wait—on average—for one proton to be transmitted? (b) How long would you have to wait if the beam consisted of electrons rather than protons?

Question: An electron with total energy $\mathit{E}\mathbf{=}\mathbf{5}\mathbf{.}\mathbf{1}\mathbf{}\mathbf{eV}$approaches a barrier of height ${\mathit{U}}_{\mathbf{b}}\mathbf{=}\mathbf{6}\mathbf{.}\mathbf{8}\mathbf{}\mathbf{eV}$and thickness $\mathit{L}\mathbf{=}\mathbf{750}\mathbf{}\mathbf{pm}$.What percentage change in the transmission coefficient $\mathit{T}$occurs for a 1.0% change in (a) the barrier height, (b) the barrier thickness, and (c) the kinetic energy of the incident

electron?

Question: The current of a beam of electrons, each with a speed of $\mathbf{1}\mathbf{.}\mathbf{200}\mathbf{\times }{\mathbf{10}}^{\mathbf{3}}\mathbf{}\mathbf{m}\mathbf{/}\mathbf{s}$, is $\mathbf{9}\mathbf{.}\mathbf{000}\mathbf{}\mathbf{mA}$. At one point along its path, the beam

encounters a potential barrier of height $\mathbf{4}\mathbf{.}\mathbf{719}\mathbf{}\mathbf{\mu V}$and thickness $\mathbf{200}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{nm}$. What is the transmitted current?

Question: Figure 38-13 shows that because of Heisenberg’s uncertainty

principle, it is not possible to assign an $\mathit{x}$coordinate to the positionof a free electron moving along an $\mathit{x}$axis. (a) Can you assign a $\mathit{y}$or a $\mathit{z}$coordinate? (Hint:The momentum of the electron has no $\mathit{y}$or $\mathit{z}$component.) (b) Describe the extent of the matter wave in threedimensions.

A light detector (your eye) has an area of $\mathbf{2}\mathbf{.}\mathbf{00}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{6}}\mathbf{}{\mathbf{m}}^{\mathbf{2}}$and absorbs 80% of the incident light, which is at wavelength 500 nm. The detector faces an isotropic source, 3.00 m from the source. If the detector absorbs photons at the rate of exactly$\mathbf{4}\mathbf{.}\mathbf{000}\mathbf{}{\mathbf{s}}^{\mathbf{-}\mathbf{1}}$at what power does the emitter emit light?