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Multiple Choice
Suppose a certain star has a temperature of At what wavelength will this star emit the most energy?
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Verified step by step guidance
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Understand that the problem is asking for the wavelength at which the star emits the most energy. This is related to the concept of blackbody radiation, where the peak wavelength is determined by the temperature of the star.
Use Wien's Displacement Law, which states that the wavelength of maximum emission, \( \lambda_{max} \), is inversely proportional to the temperature \( T \) of the blackbody. The formula is \( \lambda_{max} = \frac{b}{T} \), where \( b \) is Wien's constant, approximately \( 2.897 \times 10^{-3} \) m·K.
Substitute the given temperature of the star, \( T = 7000 \) K, into Wien's Displacement Law to find \( \lambda_{max} \). The calculation will be \( \lambda_{max} = \frac{2.897 \times 10^{-3}}{7000} \) meters.
Convert the result from meters to nanometers, since the options provided are in nanometers. Remember that 1 meter equals 1,000,000,000 nanometers.
Compare the calculated wavelength in nanometers to the given options (110 nm, 200 nm, 290 nm, 490 nm, 580 nm) to identify the closest match to the calculated \( \lambda_{max} \).