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Chapter 3: Q19E (page 93)

What wavelength of light is necessary to produce photoelectron of speed 2×108mswith a magnesium target?

Short Answer

Expert verified

The wavelength of light necessary to produce photoelectron of speed 2×108 ms with a magnesium target is 82.5 nm.

Step by step solution

01

Converting into joules.

The energy of the photon is, E=hcλ . The Kinetic energy of the photon from the zinc plate is given by: KEmax=E-φ Here φ is the work function.

Now reforming the expression, we have,

λ=hc12mλ2+f

Because magnesium's work function potential is 3.7 eV, it must first be converted to Joules:

(3.7eV)1.6×10−14 J1 cV=5.92×10−11J

02

Determine the value of wavelength.

Substituting the value to calculate the value of wavelength,

λ=(6.63×10−14 Js)3×102 ms12(9.1×10−13 kg)2×106 ms2+5.92×10−17 J=8.25×10−8 m=82.5nm

Hence the value of wavelength is 82.5 nm.

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Most popular questions from this chapter

Verify that the Chapter 2 formula ΔKE=-mc2 applies in Example 3.4.

A television picture tube accelerates electrons through a potential difference of 30000 V. Find the minimum wavelength to be expected in X-rays produced in this tube. (Picture tubes incorporate shielding to control X-ray emission).

Show that the angles of scatter of the photon and electron in the Compton effect are related by the following formula:

cotθ2=(1+hmcλ)tanϕ

A 940kHz radio station broadcasts of power. How many photons emanate from the transmitting antenna every second?

A bedrock topic in quantum mechanics is the uncertainty principle. It is discussed mostly for massive objects in Chapter 4, but the idea also applies to light: Increasing certainty in knowledge of photon position implies increasing uncertainty in knowledge of its momentum, and vice versa. A single-slit pattern that is developed (like the double-slit pattern of Section 3.6) one photon at a time provides a good example. Depicted in the accompanying figure, the pattern shows that pho tons emerging from a narrow slit are spreadall-over; a photon's x-component of momentum can be any value over a broad range and is thus uncertain. On the other hand, the x -coordinate of position of an emerging photon covers a fairly small range, for w is small. Using the single-slit diffractionformula nλ=wsinθ , show that the range of likely values of px, which is roughly psinθ , is inversely proportional to the range w of likely position values. Thus, an inherent wave nature implies that the precisions with which the particle properties of position and momentum can be known are inversely proportional.
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