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Chapter 7: Problem 23

What type of relationship (direct or inverse) exists between wavelength, frequency, and photon energy? What does a photon energy unit of a joule equal?

Short Answer

Expert verified
An inverse relationship exists between wavelength and frequency, as well as between wavelength and photon energy. A direct relationship exists between frequency and photon energy. A photon energy unit of one joule (J) represents the energy carried by a single photon, with 1 J being equal to 1 newton-meter (Nm).

Step by step solution

01

Relationship between wavelength and frequency

The wavelength (λ) and frequency (ν) of a wave are related by the formula: \[ c = λν \] where \(c\) is the speed of light in a vacuum (\(3.0 × 10^8\) m/s). Since the speed of light is a constant, the relationship between the wavelength and frequency is an inverse one: As the wavelength of a wave increases, its frequency decreases, and vice versa.
02

Relationship between photon energy and frequency

The energy of a photon (E) is related to its frequency (ν) by the formula: \[ E = hν \] where \(h\) is the Planck constant (\(6.626 × 10^{-34}\) Js). The relationship between photon energy and frequency is a direct one: As the frequency of a wave increases, its energy also increases, and vice versa.
03

Relationship between photon energy and wavelength

Combining the equations for the speed of light and the energy of a photon gives us an equation that relates photon energy with wavelength: \[ E = \frac{hc}{λ} \] Here, the relationship between photon energy and wavelength is an inverse one: As the wavelength of a wave increases, its energy decreases, and vice versa.
04

Photon energy unit of a joule

A joule (J) is the unit of energy in the International System of Units (SI) and is defined as the amount of work done when a force of one newton is applied over a distance of one meter in the direction of the force: \[ 1 J = 1 Nm \] In the context of this problem, photon energy is also given in joules. Therefore, a photon energy unit of one joule represents the energy that a single photon carries.

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Most popular questions from this chapter

In the ground state of mercury, Hg, a. how many electrons occupy atomic orbitals with \(n=3 ?\) b. how many electrons occupy \(d\) atomic orbitals? c. how many electrons occupy \(p_{z}\) atomic orbitals? d. how many electrons have spin "up" " \(\left(m_{s}=+\frac{1}{2}\right) ?\)

The work function of an element is the energy required to remove an electron from the surface of the solid element. The work function for lithium is 279.7 kJ/mol (that is, it takes 279.7 kJ of energy to remove one mole of electrons from one mole of Li atoms on the surface of Li metal). What is the maximum wavelength of light that can remove an electron from an atom on the surface of lithium metal?

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