How To Calculate The Energy of a Photon Given Frequency & Wavelength in nm Chemistry

TL;DR

Learn how to calculate the energy of a photon using different approaches, including frequency and wavelength, and explore sample calculations.

Transcript

in this tutorial we're going to focus on the different ways in which you can calculate the energy of a photon so here's the first type of problem that you might see so if you're given a frequency how can we calculate the energy of a photon you need to use this equation energy is equal to planck's constant times the frequency now the value of planck... Read More

Key Insights

• 🫤 Photon energy can be calculated using the equations E = hν or E = hc/λ, depending on whether frequency or wavelength is given.
• ✖️ To convert frequency from gigahertz to hertz, multiply by 10^9.
• 🤒 To convert wavelength from nanometers to meters, multiply by 10^-9.
• ✖️ The energy per photon can be multiplied by the number of moles or grams of photons to calculate the total energy emitted.
• #️⃣ Avogadro's number is used to convert from moles to photons.
• 🙂 Planck's constant (h) is 6.626×10^-34 J·s, and the speed of light (c) is 3×10^8 m/s.

Questions & Answers

Q: How can we calculate the energy of a photon given its frequency?

To calculate photon energy using frequency, multiply Planck's constant (6.626×10^-34) by the given frequency. For example, if the frequency is 275 gigahertz, convert it to hertz (275 × 10^9) and calculate the energy using E = (6.626×10^-34) × (275 × 10^9).

Q: How can we calculate the energy of a photon given its wavelength in nanometers?

Use the equation E = (6.626×10^-34) × (3×10^8) divided by the wavelength in meters. Convert nanometers to meters by multiplying by 10^-9. For example, if the wavelength is 500 nanometers, the energy of the photon can be calculated as (6.626×10^-34) × (3×10^8) divided by (500 × 10^-9).

Q: How do we calculate the energy of multiple photons?

Start by calculating the energy of a single photon using the given wavelength or frequency. Then, if you have the number of moles of photons, multiply it by Avogadro's number (6.022×10^23) to convert to photons. Finally, multiply the energy per photon by the number of photons to find the total energy.

Q: How do we calculate the total energy emitted by a sample of carbon atoms?

Calculate the energy per photon based on the given wavelength. Convert the sample mass of carbon to moles by dividing by the atomic mass (12 grams). Assuming one photon is emitted per carbon atom, multiply the moles by Avogadro's number and then multiply by the energy per photon to get the total energy emitted.

Summary & Key Takeaways

• Method 1: Calculate photon energy using the equation E = hν, where E is energy, h is Planck's constant, and ν is frequency.

• Method 2: Calculate photon energy using the equation E = hc/λ, where c is the speed of light and λ is wavelength.

• Method 3: Calculate the total energy of multiple photons by multiplying the energy per photon by the number of moles or grams of photons.