Calculate The Number of Photons Having A Wavelength of 10.0

Introduction

Photons are the fundamental particles of light and other electromagnetic radiation. Each photon carries a specific amount of energy determined by its wavelength. The relationship between photon energy and wavelength is described by Planck's equation:

Where:

• E is the energy of a photon (in joules)
• h is Planck's constant (6.626 × 10⁻³⁴ J·s)
• c is the speed of light (2.998 × 10⁸ m/s)
• λ is the wavelength of the photon (in meters)

When energy is transferred at a specific wavelength, the number of photons can be calculated by dividing the total energy by the energy of a single photon.

How to Calculate

To determine the number of photons at a specific wavelength, follow these steps:

1. Identify the wavelength of the photons (λ) in nanometers (nm)
2. Convert the wavelength to meters (1 nm = 1 × 10⁻⁹ m)
3. Calculate the energy of a single photon using Planck's equation
4. Determine the total energy being transferred
5. Divide the total energy by the energy of a single photon to find the number of photons

Example Calculation

Let's calculate the number of photons with a wavelength of 10.0 nm when 1 joule of energy is transferred.

1. Convert wavelength to meters: 10.0 nm = 1 × 10⁻⁸ m
2. Calculate photon energy:
   E = (6.626 × 10⁻³⁴ J·s) × (2.998 × 10⁸ m/s) / (1 × 10⁻⁸ m) E ≈ 1.986 × 10⁻¹⁵ J
3. Calculate number of photons:
   Number of photons = Total energy / Photon energy Number of photons = 1 J / (1.986 × 10⁻¹⁵ J) ≈ 5.035 × 10¹⁴ photons

Therefore, approximately 5.035 × 10¹⁴ photons are emitted or absorbed when 1 joule of energy is transferred at a wavelength of 10.0 nm.