Understanding the Relationship
* Energy, Wavelength, and Frequency: These properties of light are interconnected. The energy of a photon is directly proportional to its frequency and inversely proportional to its wavelength. This relationship is described by the following equations:
* E = hν (where E is energy, h is Planck's constant, and ν is frequency)
* c = λν (where c is the speed of light, λ is wavelength, and ν is frequency)
Calculations
1. Planck's Constant: Planck's constant (h) is a fundamental constant in physics: h = 6.626 x 10^-34 J·s
2. Energy: You've provided the energy (E) as 1.410^-21 J (assuming this is in Joules).
3. Frequency (ν):
* Rearrange the first equation (E = hν) to solve for frequency: ν = E/h
* Substitute the values: ν = (1.410^-21 J) / (6.626 x 10^-34 J·s)
* Calculate: ν ≈ 2.12 x 10^12 Hz (Hertz)
4. Wavelength (λ):
* Rearrange the second equation (c = λν) to solve for wavelength: λ = c/ν
* Use the speed of light (c) in a vacuum: c = 3 x 10^8 m/s
* Substitute the values: λ = (3 x 10^8 m/s) / (2.12 x 10^12 Hz)
* Calculate: λ ≈ 1.41 x 10^-4 m (or 141 micrometers)
Result
* Frequency: 2.12 x 10^12 Hz
* Wavelength: 1.41 x 10^-4 m (141 micrometers)
Important Note: Make sure the energy you provide is in units of Joules (J) for this calculation to be accurate.
