A photon of green light has a wavelength of $520$ nm. Find the photon's frequency, magnitude of momentum, and energy. Express the energy in both joules and electron volts.

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To find the frequency of the photon, use the formula $ c = \lambda \nu $, where $ c $ is the speed of light (approximately $ 3 \times 10^8 $ m/s), $ \lambda $ is the wavelength (520 nm, which needs to be converted to meters), and $ \nu $ is the frequency. Rearrange the formula to solve for frequency: $ \nu = \frac{c}{\lambda} $.

Convert the wavelength from nanometers to meters by using the conversion factor $ 1 \text{ nm} = 1 \times 10^{-9} \text{ m} $. Thus, $ 520 \text{ nm} = 520 \times 10^{-9} \text{ m} $.

To find the momentum of the photon, use the formula $ p = \frac{h}{\lambda} $, where $ h $ is Planck's constant (approximately $ 6.626 \times 10^{-34} \text{ J} \cdot \text{s} $) and $ \lambda $ is the wavelength in meters.

To find the energy of the photon in joules, use the formula $ E = h \nu $, where $ h $ is Planck's constant and $ \nu $ is the frequency you calculated earlier.

To convert the energy from joules to electron volts, use the conversion factor $ 1 \text{ eV} = 1.602 \times 10^{-19} \text{ J} $. Divide the energy in joules by this conversion factor to get the energy in electron volts.

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Key Concepts

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

Wave-Particle Duality

Wave-particle duality is the concept that every particle or quantum entity exhibits both wave and particle properties. For photons, this means they have a wavelength and can also be described by their momentum and energy. Understanding this duality is crucial for calculating the frequency, momentum, and energy of a photon.

Frequency-Wavelength Relationship

The frequency-wavelength relationship is described by the equation c = λν, where c is the speed of light, λ is the wavelength, and ν is the frequency. This relationship allows us to calculate the frequency of a photon when its wavelength is known, using the constant speed of light in a vacuum, approximately 3 x 10^8 m/s.

Photon Energy and Momentum

Photon energy is given by E = hν, where h is Planck's constant (6.626 x 10^-34 Js) and ν is the frequency. Momentum is calculated using p = E/c. Energy can be expressed in joules or electron volts (1 eV = 1.602 x 10^-19 J). These formulas are essential for determining the energy and momentum of a photon from its frequency.