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Blackbody Radiation Question 1: Limit of Planck's Law is 0 as Wavelength Approaches 0 or ∞ https://youtu.be/8gcdHAhVVG0 In this video I show by using l'Hospital's Rule for indeterminate limits, that Planck's Law for blackbody radiation approaches zero as…
Blackbody Radiation Question 2: Planck's Law Approximates Rayleigh-Jeans Law at Large Wavelengths https://youtu.be/p2a4QGnzlm0

In this video I show that using just the first term for the Taylor series expansion of the exponential function in Planck's Law, it becomes Rayleigh-Jeans Law. This results in a good approximation for Rayleigh-Jeans Law at large wavelengths since the extra terms of the Taylor series become very small.

#math #physics #QuantumMechanics #science #education
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Blackbody Radiation Question 2: Planck's Law Approximates Rayleigh-Jeans Law at Large Wavelengths https://youtu.be/p2a4QGnzlm0 In this video I show that using just the first term for the Taylor series expansion of the exponential function in Planck's Law…
Blackbody Radiation Questions 3,4: Comparing Planck's Law to Rayleigh-Jeans Law for the Sun https://youtu.be/SL3z_KJ7yPw

In this video I graph out the blackbody radiation energy density for the Sun using both Planck's Law and the classical Rayleigh-Jeans Law. At large wavelengths, both models are similar but at short wavelengths the classical theory diverges wildly to infinity. This was the cause of the Ultraviolet Catastrophe.

#math #science #physics #QuantumMechanics #education