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In Rayleigh scattering, the intensity of scattered light is inversely proportional to the fourth power of wavelength (scattering proportional to 1/lambda⁴). It is given that violet light (lambda = 4 * 10^(-7) m) is scattered 10 times as much as red light (lambda = 7 * 10^(-7) m). The relative scattering intensities for different colours are: Violet = 10, Blue = 6, Green = 3, Yellow = 2.5, Orange = 2, Red = 1. Using these data, find the wavelength of yellow light in the form alpha * 10^(-7) m. What is alpha?

1. 2.8
2. 5.6
3. 7.0
4. 4.0

Correct answer: 5.6

Solution

From Rayleigh scattering: S proportional to 1/lambda⁴. So S_yellow / S_red = (lambda_red / lambda_yellow)⁴. Given S_yellow = 2.5 and S_red = 1: (lambda_red / lambda_yellow)⁴ = 2.5. lambda_yellow = lambda_red / (2.5)^(1/4). Now 2.5^(1/4): sqrt(2.5) = 1.581, sqrt(1.581) = 1.257. lambda_yellow = 7 * 10^(-7) / 1.257 = 5.57 * 10^(-7) m approximately 5.6 * 10^(-7) m. So alpha = 5.6.

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