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Chapter 38: Q. 47 (page 1115)

The electron interference pattern of Figure 38.12 was made by shooting electrons with 50keVof kinetic energy through two slits spaced role="math" localid="1650737433408" 1.0渭尘apart. The fringes were recorded on a detector 1.0mbehind the slits.

a. What was the speed of the electrons? (The speed is large enough to justify using relativity, but for simplicity do this as a nonrelativistic calculation.)

b. Figure 38.12 is greatly magnified. What was the actual spacing on the detector between adjacent bright fringes?

Short Answer

Expert verified

(a) The speed of the electron isv=1.33脳108ms

(b) The actual distance between consecutive light fringes on the detector is螖测=5.47渭尘

Step by step solution

01

Given information

The kinetic energy of electrons is 50 KeV and a detector captured the fringes is 1.0 m

02

Part (a) Step 1: Given information

The electron starts at rest (or close to it), thus the kinetic energy obtained is12mv2

03

Part (a) Step 2: Finding the electron's speed using kinetic energy 

We can begin by calculating the electron's speed using kinetic energy,

Ek=mv22v=2Ekmexpressvv=2鈰�50脳103脳1.6脳10鈭�199.11脳10鈭�31v=1.33鈰�108ms

04

Part (b) Step 1: Given information

On a detector 1.0 m behind the slits, the fringes were recorded

05

Part (b) Step 2: Determine the double slit experiment, fringe spacing 

In a double slit experiment, we can now utilise an expression for fringe spacing.

螖测=尝位d位=hmv(de Broglie wavelength)螖测=Lhmvd(substitute位)螖测=1鈰�6.63脳10鈭�349.11脳10鈭�31脳1.33脳108脳1脳10鈭�6(substitute)螖测=5.47渭尘

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Most popular questions from this chapter

FIGURE Q38.12 shows the energy-level diagram of Element X.

a. What is the ionization energy of Element X?

b. An atom in the ground state absorbs a photon, then emits a photon with a wavelength of 1240 nm. What was the energy of the photon that was absorbed?

c. An atom in the ground state has a collision with an electron, then emits a photon with a wavelength of 1240 nm. What conclusion can you draw about the initial kinetic energy of the electron?

(a). What is the de Broglie wavelength of a 200gbaseball with a speed of 30m/s?

(b). What is the speed of a 200gbaseball with a de Broglie wavelength of 0.20nm?

a. Calculate the de Broglie wavelength of the electron in the n=1,2,and3states of the hydrogen atom. Use the information in Table 38.2 .

b. Show numerically that the circumference of the orbit for each of these stationary states is exactly equal to n de Broglie wavelengths.

c. Sketch the de Broglie standing wave for then=3 orbit

a. Determine the energy, in eV, of a photon with a 550 nm wavelength.

b. Determine the wavelength of a 7.5 keV x-ray photon.

Which metals in Table 38.1 exhibit the photoelectric effect for (a) light with位=400nm and (b) light with 位=250nm?
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