The maximum wavelength of light that a certain silicon photocell can detect is 1.111.11 mm. What is the energy gap (in electron volts) between the valence and conduction bands for this photocell?

Step 1: Understand the relationship between the wavelength of light and its energy. The energy of a photon is given by the equation: E=hc/λ, where E is the energy of the photon, h is Planck's constant (6.626×10⁻34 J·s), c is the speed of light (3.00×10⁸ m/s), and λ is the wavelength of the light. Step 2: Convert the given wavelength from millimeters to meters. Since 1 mm = 10⁻3 m, the wavelength λ is 1.11×10⁻3 m. Step 3: Substitute the values of h, c, and λ into the equation E=hc/λ to calculate the energy of the photon in joules. Step 4: Convert the energy from joules to electron volts (eV). Use the conversion factor: 1 eV = 1.602×10⁻19 J. Step 5: The calculated energy in electron volts represents the energy gap between the valence and conduction bands for the silicon photocell. This is the final result.

Ch 42: Molecules and Condensed Matter

Young & Freedman Calc - University Physics 15th Edition

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Young & Freedman Calc 15th Edition

Ch 42: Molecules and Condensed Matter

Problem 15a

Chapter 41, Problem 15a

The maximum wavelength of light that a certain silicon photocell can detect is $1.11$ mm. What is the energy gap (in electron volts) between the valence and conduction bands for this photocell?

Verified step by step guidance

Step 1: Understand the relationship between the wavelength of light and its energy. The energy of a photon is given by the equation:

E = h c / λ

, where

E

is the energy of the photon,

h

is Planck's constant (

6.626 \times 10 ⁻ 34

J·s),

c

is the speed of light (

3.00 \times 10 ⁸

m/s), and

λ

is the wavelength of the light.

Step 2: Convert the given wavelength from millimeters to meters. Since 1 mm =

10 ⁻ 3

m, the wavelength

λ

1.11 \times 10 ⁻ 3

Step 3: Substitute the values of

h

c

, and

λ

into the equation

E = h c / λ

to calculate the energy of the photon in joules.

Step 4: Convert the energy from joules to electron volts (eV). Use the conversion factor:

1

eV =

1.602 \times 10 ⁻ 19

Step 5: The calculated energy in electron volts represents the energy gap between the valence and conduction bands for the silicon photocell. This is the final result.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Energy Gap

The energy gap, or band gap, is the energy difference between the valence band and the conduction band in a semiconductor. It determines the energy required for an electron to transition from a bound state in the valence band to a free state in the conduction band, allowing for electrical conduction. The size of the energy gap influences the material's electrical and optical properties, including its ability to absorb light.

Photon Energy

Photon energy is the energy carried by a single photon, which can be calculated using the equation E = hc/λ, where E is energy, h is Planck's constant, c is the speed of light, and λ is the wavelength. In the context of the photocell, the maximum wavelength of light it can detect corresponds to the minimum energy required to excite an electron across the energy gap. Thus, understanding photon energy is crucial for determining the energy gap.

Semiconductor Physics

Semiconductor physics studies materials that have electrical conductivity between that of conductors and insulators. In semiconductors like silicon, the behavior of charge carriers (electrons and holes) is influenced by the energy gap. The properties of semiconductors are essential for understanding devices like photocells, which rely on the absorption of light to generate electrical signals.

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