Final answer:
The lowest possible temperature of the object can be estimated using Wien's law, which states that the wavelength at which the object emits its maximum energy is inversely proportional to its temperature. We get 31,780 Kelvin.
Step-by-step explanation:
The lowest possible temperature can be estimated using Wien's law from Radiation and Spectra.
Wien's law states that the wavelength at which the object emits its maximum energy is inversely proportional to its temperature. The formula is λmax = b / T, where λmax is the wavelength, b is Wien's constant, and T is the temperature in Kelvin.
To estimate the lowest temperature, we need to find the wavelength at which the object emits its maximum energy. The question states that the radiation emitted by the object has a wavelength spectrum that can potentially ionize hydrogen atoms. Hydrogen is ionized by radiation with wavelengths shorter than 91.2 nm. Therefore, the maximum energy is emitted at 91.2 nm.
Using this information, we can solve for the temperature:
λmax = b / T
91.2 nm = b / T
T = b / 91.2 nm
Substituting the value of b (2.898 × 10^-3 mK) into the equation:
T ≈ (2.898 × 10^-3 mK) / (91.2 × 10^-9 m)
T ≈ 31,780 K
Therefore, the lowest possible temperature of the object is approximately 31,780 Kelvin.