Ch.13 - Solids & Modern Materials

Problem 67

Chapter 13, Problem 67

Does a photon of red light with a frequency of 4.29⨉10¹⁴ Hz have sufficient energy to promote an electron from the valence band to the conduction band in a sample of silicon (the band gap in silicon is 1.11 eV)?

Verified step by step guidance

Identify the energy of the photon using the formula: \( E = h \cdot f \), where \( h \) is Planck's constant \( 6.626 \times 10^{-34} \text{ J} \cdot \text{s} \) and \( f \) is the frequency of the photon.

Convert the energy from joules to electronvolts (eV) using the conversion factor: \( 1 \text{ eV} = 1.602 \times 10^{-19} \text{ J} \).

Compare the energy of the photon in eV to the band gap energy of silicon, which is 1.11 eV.

Determine if the photon's energy is greater than or equal to the band gap energy to decide if it can promote an electron from the valence band to the conduction band.

Conclude whether the photon has sufficient energy based on the comparison.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

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

Photon Energy

The energy of a photon is directly related to its frequency and can be calculated using the equation E = hν, where E is energy, h is Planck's constant (6.626 x 10^-34 J·s), and ν is the frequency of the light. For red light with a frequency of 4.29 x 10^14 Hz, this relationship allows us to determine if the photon has enough energy to affect electron transitions in materials.

Band Gap Energy

The band gap energy is the energy difference between the valence band and the conduction band in a semiconductor. In silicon, this band gap is approximately 1.11 eV, which means that an electron must gain at least this amount of energy to transition from the valence band to the conduction band, allowing for electrical conductivity.

Energy Conversion

To determine if the photon can promote an electron in silicon, we must convert the photon's energy from electron volts (eV) to joules (J) or vice versa. Since 1 eV is equivalent to 1.602 x 10^-19 J, this conversion is essential for comparing the energy of the photon with the band gap energy of silicon to see if the transition is possible.

Recommended video:

Guided course

01:56

Conversion Factors

Related Practice

Textbook Question

How many molecular orbitals are present in the conduction band of a lithium crystal with a mass of 11.2 g?

Textbook Question

A substance has a band gap of 6.9 eV at 273 K. Is this substance best classified as an insulator, a semiconductor, or a metal?

Textbook Question

Indicate if each solid forms an n-type or a p-type semiconductor.

a. silicon doped with gallium

b. germanium doped with antimony

Textbook Question

Teflon is an addition polymer formed from the monomer shown here. Draw the structure of the polymer.

Textbook Question

Saran, the polymer used to make saran wrap, is an addition polymer formed from two monomers—vinylidene chloride and vinyl chloride. Draw the structure of the polymer. (Hint: The monomers alternate.)

Does a photon of red light with a frequency of 4.29⨉1014 Hz have sufficient energy to promote an electron from the valence band to the conduction band in a sample of silicon (the band gap in silicon is 1.11 eV)?

Verified video answer for a similar problem:

Key Concepts

Photon Energy

Band Gap Energy

Energy Conversion

Does a photon of red light with a frequency of 4.29⨉10¹⁴ Hz have sufficient energy to promote an electron from the valence band to the conduction band in a sample of silicon (the band gap in silicon is 1.11 eV)?