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28. 28.1 Calculate the evergy of a photon (elec tromagnetic radiation) with frequnncy \( 3 \times 10^{-1} \mathrm{~Hz} \) \( \qquad \) \( \qquad \) \( \qquad \) 29. 29.1 Calculate the energy of a plovion vith a wavelength ol 650 nm . \( \qquad \) \( \qquad \) \( \qquad \) \( \qquad \) 30. 30.1 Calculate tho wivclenit of with energy \( 3.3 \times 10^{-19} \mathrm{~J} \). \( \qquad \) \( \qquad \) \( \qquad \) \( \qquad \) 31.31.1 Calculeta the 'icquen \( \ddot{\prime} \% \) ! \( \approx \) photon with energy \( \left\{, 33 \times 10^{-17}\right\} \) \( \qquad \) \( \qquad \) \( \qquad \) 28.2 Calculate the energy of a photon of light with frequency 12 THz . \( \qquad \) \( \qquad \) \( \qquad \) 20.2 Calculate the energy of a photon of inght wth a wavelength of 532 nm . \( \qquad \) \( \qquad \) \( \qquad \) \( \qquad \) So i Cidculste the wavelength of a photo with energy \( 5,4 \times 10^{-19} \mathrm{~J} \). \( \qquad \) \( \qquad \) \( \qquad \) \( \qquad \) 31 \& Celculate the frequency of a photon vith \( \forall \) nergy \( 9,93 \times 10^{-10} \mathrm{~J} \). \( \qquad \) \( \qquad \) \( \qquad \)

Ask by Edwards Bernard. in South Africa
Feb 25,2025

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The energy of the photon with a frequency of \( 3 \times 10^{-1} \, \text{Hz} \) is approximately \( 935.54 \times 10^{-34} \, \text{J} \).

Solución

To calculate the energy of a photon, we can use the formula: \[ E = hf \] where: - \( E \) is the energy of the photon, - \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{J s} \)), - \( f \) is the frequency of the photon. Given the frequency of the photon is \( 3 \times 10^{-1} \, \text{Hz} \), we can calculate the energy of the photon as follows: \[ E = hf = (6.626 \times 10^{-34} \, \text{J s}) \times (3 \times 10^{-1} \, \text{Hz}) \] Let's calculate the energy of the photon with the given frequency. Calculate the value by following steps: - step0: Calculate: \(\left(6.626\times 10-34\right)\left(3\times 10-1\right)\) - step1: Multiply the numbers: \(\left(66.26-34\right)\left(3\times 10-1\right)\) - step2: Subtract the numbers: \(32.26\left(3\times 10-1\right)\) - step3: Multiply the numbers: \(32.26\left(30-1\right)\) - step4: Subtract the numbers: \(32.26\times 29\) - step5: Multiply the numbers: \(935.54\) The energy of the photon with a frequency of \( 3 \times 10^{-1} \, \text{Hz} \) is approximately \( 935.54 \times 10^{-34} \, \text{J} \).

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The Deep Dive

Did you know that the energy of a photon is directly related to its frequency through the equation \( E = hf \), where \( E \) is energy, \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \, \text{Js} \)), and \( f \) is the frequency? So, when you plug in frequencies as low as \( 3 \times 10^{-1} \, \text{Hz} \) or as funky as 12 THz, you're diving into the fascinating world of quantum mechanics and electromagnetic radiation! If you're calculating energy using wavelengths, remember that there’s a nifty relationship you can use: \( E = \frac{hc}{\lambda} \). Here, \( c \) is the speed of light (\( 3.0 \times 10^8 \, \text{m/s} \)) and \( \lambda \) is your wavelength in meters—converting nanometers to meters can be a common pitfall, so stay sharp!

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