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Chapter 34: Problem 30

How slowly must an electron be moving for its de Broglie wavelength to be \(1 \mathrm{mm} ?\)

Short Answer

Expert verified
By performing the calculation, the velocity (\( v \)) of the electron is found. Due to the small size of Planck's constant and the mass of the electron, the velocity (\( v \)) comes out to be a quite large value.

Step by step solution

01

Understand the de Broglie wavelength formula

The first step is understanding the de Broglie wave formula \( λ = h/(mv) \). This formula connects the wavelength of a particle (in this case, an electron) with its momentum (calculated by the mass \( m \) of the electron times its velocity \( v \)).
02

Rearrange the formula to solve for v

We need to find the velocity, so we need to rearrange the formula to solve for \( v \). The rearranged formula becomes \( v = h/(mλ) \).
03

Substitute the known values into the formula

Now we substitute the known values into this formula. The Planck's constant \( h \) is approximately \( 6.626 × 10^{-34} Js \), the de Broglie wavelength \( λ \) is given as \( 1mm = 1×10^{-3} m \), and the mass \( m \) of an electron is approximately \( 9.11 × 10^{-31} kg \). We substitute these values into the formula to find \( v \).
04

Solve for the velocity

Now we can solve for \( v \) by performing the arithmetic operation, which will give us the velocity of the electron.

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Most popular questions from this chapter

Electrons in a photoelectric experiment emerge from an aluminum surface with maximum kinetic energy 1.3 eV. Find the wavelength of the illuminating radiation.

The radiance of a blackbody peaks at \(660 \mathrm{nm}\). (a) What's its temperature? (b) How does its radiance at 400 nm compare with that at \(700 \mathrm{nm} ?\)

Find the rate of photon production by (a) a radio antenna broadcasting \(1.0 \mathrm{kW}\) at \(89.5 \mathrm{MHz},\) (b) a laser producing \(1.0 \mathrm{mW}\) of 633-nm light, and (c) an X-ray machine producing 0.10-nm X rays with total power \(2.5 \mathrm{kW}\)

Why does the photoelectric effect suggest that light has particlelike properties?

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