Chapter 6, Problem 12PS

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Chapter
Section

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

# You are an engineer designing a switch that works by the photoelectric effect. The metal you wish to use in your device requires 6.7 × 10‒19 J/atom to remove an electron. Will the switch work if the light falling on the metal has a wavelength of 540 nm or greater? Why or why not?

Interpretation Introduction

Interpretation: The switch whether works or not has to be determined and explained when the light falling on the metal has a wavelength of 540nm or more and the reason.

Concept introduction:

• Electromagnetic radiations are a type of energy surrounding us. They are of different types like radio waves, IR, UV, X-ray etc.
• The violet and red light lies in the visible light where violet light is between 390nm and 455nm whereas red light is between 622nm and 780nm.
• Planck’s equation,

E=where, E=energyh=Planck'sconstantν=frequency

The energy increases as the wavelength of the light decrease. Also the energy increases as the frequency of the light increases.

• The frequency of the light is inversely proportional to its wavelength.

ν=cλwhere, c=speedoflightν=frequencyλ=wavelength

• Photoelectric effect: Electrons get ejected if a ray of light hits on the surface of metal when the light has adequately high frequency. A minimum frequency is required for the light to eject the electrons called threshold frequency
Explanation

Given,

The wavelength violet light is 410â€‰nmâ€‰=â€‰4.10Â Ã—â€‰10â€‰âˆ’7m

Â Â Planck'sâ€‰constant,hâ€‰=â€‰6.626â€‰Ã—â€‰10â€‰âˆ’34â€‰J.sTheÂ speedÂ ofÂ light,câ€‰=â€‰2.998â€‰Ã—â€‰10â€‰8â€‰m/sEnergy,â€‰Eâ€‰=â€‰6.7â€‰Ã—â€‰10âˆ’19â€‰J/atom

• The energy per photon of light is calculated by using the equation,

â€‚Â Eâ€‰=â€‰hÎ½

According to photoelectric effect a minimum frequency is required for the light to eject the electrons called threshold frequency. The electrons get ejected from the metal surface only if the frequency is equal to or above the particular frequency.

Hence, threshold frequency can be calculated by

â€‚Â Thresholdâ€‰frequency,â€‰Î½â€‰=â€‰Eh=â€‰(6.7â€‰Ã—â€‰10âˆ’19â€‰J/atom)(6.626â€‰Ã—â€‰10â€‰âˆ’34â€‰J.s)=â€‰1.01â€‰Ã—â€‰1015â€‰sâˆ’1

Threshold frequency is 1.01â€‰Ã—â€‰1015â€‰sâˆ’1

• The frequency of light falling is calculated by using the equation,

The wavelength of light falling is 540â€‰nmâ€‰=â€‰5

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