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Determine the energy of a photon of EM radiation with a wavelength of 600 nm .

Ask by Hardy Salinas. in South Africa
Feb 25,2025

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The energy of a photon with a wavelength of 600 nm is approximately 3.31 × 10⁻¹⁹ joules or about 2.07 electron volts.

Solución

To determine the energy of a photon with a given wavelength, we use the equation:   E = (h × c) / 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), • λ is the wavelength in meters. Step 1: Convert the wavelength from nanometers to meters.   Since 1 nm = 1 × 10⁻⁹ m, a wavelength of 600 nm is:   λ = 600 nm = 600 × 10⁻⁹ m = 6.00 × 10⁻⁷ m Step 2: Substitute the values into the equation.   E = (6.626 × 10⁻³⁴ J·s × 3.00 × 10⁸ m/s) / (6.00 × 10⁻⁷ m) Step 3: Compute the numerator.   Numerator = (6.626 × 10⁻³⁴ J·s) × (3.00 × 10⁸ m/s)        = 1.9878 × 10⁻²⁵ J·m Step 4: Divide by the wavelength.   E = (1.9878 × 10⁻²⁵ J·m) / (6.00 × 10⁻⁷ m)     = 3.313 × 10⁻¹⁹ J Therefore, the energy of a photon with a wavelength of 600 nm is approximately 3.31 × 10⁻¹⁹ joules. (Optional conversion to electron volts) Since 1 eV = 1.602 × 10⁻¹⁹ J:   E ≈ (3.31 × 10⁻¹⁹ J) / (1.602 × 10⁻¹⁹ J/eV) ≈ 2.07 eV So, the photon has an energy of about 2.07 eV.

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Beyond the Answer

To find the energy of a photon, you can use the equation \(E = \frac{hc}{\lambda}\), where \(E\) is energy, \(h\) is Planck's constant (approximately \(6.626 \times 10^{-34} \, \text{J s}\)), \(c\) is the speed of light (approximately \(3.00 \times 10^8 \, \text{m/s}\)), and \(\lambda\) is the wavelength (in meters). So, for a wavelength of 600 nm (which is \(600 \times 10^{-9}\) meters), you plug the numbers into the equation to find that the energy of the photon is approximately \(3.31 \times 10^{-19} \, \text{J}\). Want to impress your friends at a party? Throw in some trivia about how visible light ranges from about 400 nm (violet) to 700 nm (red) on the electromagnetic spectrum. That means your 600 nm photon is right in the middle of the rainbow - specifically in the orange-red area! If you’re a science enthusiast, consider diving into the quantum world with further reading on photon energy and its applications in technologies like solar panels. Understanding how light interacts with matter will open up a universe of exciting possibilities, from improving energy efficiency to advancing medical technologies!

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