To address your question, let's delve into the relationship between temperature and the type of radiation emitted by an object, which is indeed governed by Wien's Displacement Law. When the temperature of an object is increased, the peak wavelength of the emitted radiation shifts to shorter wavelengths. This principle is crucial in understanding why the correct answer is option A, ultraviolet (U.V.) radiation, rather than gamma rays or any other type of radiation.

Understanding Wien's Displacement Law

Wien's Displacement Law states that the wavelength at which the emission of radiation is maximized (the peak wavelength) is inversely proportional to the absolute temperature of the black body. Mathematically, it can be expressed as:

λ_max = b / T

Here, λ_max is the peak wavelength, T is the absolute temperature in Kelvin, and b is Wien's displacement constant (approximately 2898 μm·K).

Temperature Doubling and Radiation Shift

When you double the temperature of an object, you can see how the peak wavelength changes:

• If the initial temperature is T, the new temperature becomes 2T.
• According to Wien's Law, the new peak wavelength will be:
• λ'_max = b / (2T) = (1/2) * (b / T) = (1/2) * λ_max

This indicates that the peak wavelength is halved, meaning the radiation emitted shifts to a shorter wavelength.

Identifying the Radiation Region

Now, let's consider the regions of the electromagnetic spectrum:

• Gamma Rays: Wavelengths less than 0.01 nm
• X-Rays: Wavelengths from 0.01 nm to 10 nm
• Ultraviolet (U.V.): Wavelengths from 10 nm to 400 nm
• Visible Light: Wavelengths from 400 nm to 700 nm
• Infrared (I.R.): Wavelengths from 700 nm to 1 mm

When the temperature is doubled, the peak wavelength moves into the ultraviolet region, which is why option A is correct.

Why Not Gamma Rays?

While it is true that gamma rays have shorter wavelengths than ultraviolet rays, the temperature required to emit gamma radiation is extraordinarily high, far beyond typical physical conditions. For example, gamma rays are typically produced in nuclear reactions or cosmic events, not in everyday thermal radiation scenarios. Thus, while the product of wavelength and temperature is constant, the practical application of this law in thermal radiation confines us to the ultraviolet region when temperatures are doubled.

Conclusion

In summary, when the temperature of an object is doubled, the radiation emitted indeed shifts into the ultraviolet region, as dictated by Wien's Displacement Law. Gamma rays, while having shorter wavelengths, are not relevant in this context of thermal radiation. Understanding these principles helps clarify the behavior of different types of radiation in relation to temperature changes.