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Chapter 8: Problem 25

The lowest-frequency light that will produce the photoelectric effect is called the threshold frequency. (a) The threshold frequency for indium is \(9.96 \times\) \(10^{14} \mathrm{s}^{-1} .\) What is the energy, in joules, of a photon of this radiation? (b) Will indium display the photoelectric effect with UV light? With infrared light? Explain.

Short Answer

Expert verified
The energy of a photon with this frequency is \(6.604 × 10^{-19} J\). Indium will show the photoelectric effect with UV light but not with infrared light.

Step by step solution

01

Calculate the Energy of a Photon

Using the given threshold frequency for indium, \(\(9.96 \times 10^{14} s^{-1}\)\) and Planck's constant, calculate the energy of a photon by applying the energy formula \(E = hν\). So, \(E = 6.626 \times 10^{-34} Js \times 9.96 \times 10^{14} s^{-1} = 6.604 × 10^{-19} J\).
02

Identification of the Effect of UV and Infrared Light

UV light has a frequency range of \(10^{16} to 10^{15} s^{-1}\) and infrared light has a frequency from \(10^{14} to 10^{12} s^{-1}\). As indium's threshold frequency is \(9.96 \times 10^{14} s^{-1}\), it is less than the frequency of UV light and greater than the frequency of infrared light. Hence, indium will show the photoelectric effect with UV light but not with infrared light, as the frequency of infrared light is less than the threshold frequency.

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Most popular questions from this chapter

A molecule of chlorine can be dissociated into atoms by absorbing a photon of sufficiently high energy. Any excess energy is translated into kinetic energy as the atoms recoil from one another. If a molecule of chlorine at rest absorbs a photon of 300 nm wavelength, what will be the velocity of the two recoiling atoms? Assume that the excess energy is equally divided between the two atoms. The bond energy of \(\mathrm{Cl}_{2}\) is \(242.6 \mathrm{kJ} \mathrm{mol}^{-1}\)

High-pressure sodium vapor lamps are used in street lighting. The two brightest lines in the sodium spectrum are at 589.00 and \(589.59 \mathrm{nm}\). What is the difference in energy per photon of the radiations corresponding to these two lines?

Use appropriate relationships from the chapter to determine the wavelength of the line in the emission spectrum of \(\mathrm{He}^{+}\) produced by an electron transition from \(n=5\) to \(n=2\).

Without doing detailed calculations, indicate which of the following electron transitions requires the greatest amount of energy to be absorbed by a hydrogen atom: from (a) \(n=1\) to \(n=2 ;\) (b) \(n=2\) to \(n=4 ;\) (c) \(n=3\) to \(n=9 ;\) (d) \(n=10\) to \(n=1\)

What is \(\Delta E\) for the transition of an electron from \(n=5\) to \(n=2\) in a Bohr hydrogen atom? What is the frequency of the spectral line produced?
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