Respuesta :
Answer:
wavelength (λ) = 2.73 E-4 m
frecuency (f) = 1.10 E12 s-1
Explanation:
Stefan-Boltzmann law:
- intensity of the radiation for a black body (W) = σ.(T)∧4
∴ σ = 5.670 E-8 W/m²(K)∧4
∴ T = 298 K
⇒ W = (5.670 E-8 W/m²K∧4)×(298 K)∧4
⇒ W = 447.145 W/m² = 447.145 J/s.m²
assuming an area of 1 m²
⇒ W = 447.145 J/s
Rayleigh-Jeans's law:
∴ Black body radiation at a specific wavelength (Bλ(T)):
⇒ Bλ(T) = ( 2 c.k.T ) / (λ)∧4
∴ c = 3 E8 m/s.....velocity of speed
∴ k = 1.38065 E -23 J/K.........Boltzmann's constant
∴ Bλ(T) = 447.145 J/s.m²
⇒ (λ)∧4 = ((2)(3 E8 m/s)(1.38065 E-23 J/K)(298 K)) / (447.145 J/s)
⇒ λ = (5.521 E-15)∧(1/4)
⇒ λ = 2.73 E-4 m
- f = c/λ
⇒ f = (3 E8 m/s) / (2.73 E-4 m)
⇒ f = 1.10 E12 s-1
Answer:
λ(max) = = 9.7 *10^-6m
Frequency(max) = 3.09 * 10^13 /s = 3.09 * 10^13 Hz
Explanation:
Step 1: Data given
Temperature = 298 K
In order to find maximum wavelength and maximum frequency, apply Wien's Law of maximum wavelength * Temperature = 2.9*10^-3 meters * Kelvin
Step 2: Calculate wavelength
λ(max) * T = 2.9 *10^-3 m*K
λ(max) = (2.9 *10^-3 m*K)/T
λ(max) = (2.9 *10^-3 m*K)/298
λ(max) = = 9.7 *10^-6m
Step 3: Calculate frequency
Frequency(max) = c/λ(max)
Frequency(max) = 3*10^8 m/s / 9.7 *10^-6m
Frequency(max) = 3.09 * 10^13 /s = 3.09 * 10^13 Hz
