Which frequency choice is associated with the greatest scattering intensity according to Rayleigh scattering theory?

Which frequency choice is associated with the greatest scattering intensity according to Rayleigh scattering theory?

• A. Frequency raised to the second power
• B. Frequency raised to the fourth power
• C. Frequency to the first power
• D. Frequency cubed

Answer: (B)

Rayleigh scattering intensity scales with the fourth power of the light’s frequency (equivalently, it scales with the inverse fourth power of wavelength). This quartic dependence comes from how the oscillating charges in a small particle radiate: the radiated power is highly sensitive to the frequency because the induced dipole accelerates more strongly as frequency increases. As a result, higher-frequency light scatters much more than lower-frequency light, with intensity ∝ ν^4. Among the given options, the frequency raised to the fourth power represents the strongest, most rapid increase in scattering, which is why that form is associated with the greatest scattering intensity. This also explains why shorter wavelengths (higher frequencies) scatter more, giving the sky its blue color. The other options grow more slowly with frequency and do not match Rayleigh’s ν^4 dependence.

Rayleigh scattering intensity scales with the fourth power of the light’s frequency (equivalently, it scales with the inverse fourth power of wavelength). This quartic dependence comes from how the oscillating charges in a small particle radiate: the radiated power is highly sensitive to the frequency because the induced dipole accelerates more strongly as frequency increases. As a result, higher-frequency light scatters much more than lower-frequency light, with intensity ∝ ν^4. Among the given options, the frequency raised to the fourth power represents the strongest, most rapid increase in scattering, which is why that form is associated with the greatest scattering intensity. This also explains why shorter wavelengths (higher frequencies) scatter more, giving the sky its blue color. The other options grow more slowly with frequency and do not match Rayleigh’s ν^4 dependence.