Wien's Law Calculator Wavelength Spectrum

Wien's Law Formula:

\[ \lambda_{\text{max}} = \frac{b}{T} \]

Where:

\( \lambda_{\text{max}} \) — Peak wavelength (meters)
\( b \) — Wien's displacement constant (2.897 × 10⁻³ m·K)
\( T \) — Absolute temperature (Kelvin)

Peak Wavelength (λ_max):

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1. What is Wien's Law?

Wien's Law, also known as Wien's displacement law, states that the black-body radiation curve for different temperatures will peak at different wavelengths that are inversely proportional to the temperature. It's a fundamental principle in thermodynamics and astrophysics.

2. How Does the Calculator Work?

The calculator uses Wien's Law equation:

\[ \lambda_{\text{max}} = \frac{b}{T} \]

Where:

\( \lambda_{\text{max}} \) — Peak wavelength in meters
\( b \) — Wien's displacement constant (2.897 × 10⁻³ m·K)
\( T \) — Absolute temperature in Kelvin

Explanation: As the temperature of a black body increases, the peak wavelength of its emitted radiation shifts to shorter wavelengths (higher frequencies).

3. Importance of Wien's Law

Details: Wien's Law is crucial for determining the temperature of stars and other celestial bodies based on their radiation spectra. It's also used in infrared thermography, thermal imaging, and various industrial applications.

4. Using the Calculator

Tips: Enter the temperature in Kelvin (absolute temperature). The temperature must be greater than 0 K. The result will show the peak wavelength in meters.

5. Frequently Asked Questions (FAQ)

Q1: What is Wien's displacement constant?
A: Wien's displacement constant (b) is approximately 2.897771955... × 10⁻³ m·K, which relates the peak wavelength of black-body radiation to its temperature.

Q2: How is Wien's Law used in astronomy?
A: Astronomers use Wien's Law to estimate the surface temperatures of stars by measuring the wavelength at which their radiation peaks.

Q3: What are the limitations of Wien's Law?
A: Wien's Law applies specifically to black-body radiation and may not be accurate for objects that don't behave as perfect black bodies.

Q4: Can I use Celsius or Fahrenheit with this calculator?
A: No, the calculator requires temperature in Kelvin. You must convert Celsius or Fahrenheit to Kelvin first (K = °C + 273.15, K = (°F + 459.67) × 5/9).

Q5: What is the relationship between temperature and peak wavelength?
A: They have an inverse relationship - as temperature increases, the peak wavelength decreases, moving toward the blue/violet end of the spectrum.