T/F: Cooler objects radiate more of their total light at shorter wavelengths than do hotter objects.

Wien’s Displacement Law is a crucial principle in understanding blackbody radiation. It relates the temperature of an object to the wavelength at which it emits the most radiation. According to this law, as the temperature of an object increases, the peak wavelength of the emitted radiation shifts to shorter wavelengths. This is expressed mathematically as: \(\text{λ}_{max} = \frac{b}{T}\), where \(\text{λ}_{max}\) is the wavelength of maximum emission, \(T\) is the absolute temperature in kelvins, and \(b\) is Wien's displacement constant (approximately 2.898 x 10^(-3) m⋅K). In simpler terms:

• Hotter objects emit radiation that peaks at shorter wavelengths (bluer light).
• Cooler objects emit radiation that peaks at longer wavelengths (redder light).

This relationship helps explain why stars of different temperatures emit visible light in different colors.

Electromagnetic radiation encompasses a wide range of wavelengths and frequencies of light, including visible light, radio waves, and X-rays. All objects emit electromagnetic radiation as a function of their temperature.

• At higher temperatures, the emitted radiation shifts to higher frequencies and shorter wavelengths.
• At lower temperatures, the radiation shifts to lower frequencies and longer wavelengths.

Blackbody radiation is a perfect example of how an idealized object emits a specific spectrum of electromagnetic radiation based solely on its temperature. This emission includes all wavelengths, with intensities that follow a characteristic curve known as the blackbody spectrum.

The temperature of an object significantly influences its emitted radiation. Wien’s Displacement Law directly connects this: the higher the temperature, the shorter the wavelength of peak emission. For practical understanding:

• Hotter objects (like the Sun) emit most of their light at shorter wavelengths, such as visible or ultraviolet light.
• Cooler objects (like the Earth) emit most of their light at longer wavelengths, such as infrared.

This relationship is essential in fields such as astronomy and climate science, helping us determine the temperatures of distant stars and planets based on their emitted spectra. Remember: the peak wavelength and temperature are inversely related, ensuring that cooler objects radiate at longer (not shorter) wavelengths, debunking the incorrect statement in the exercise.