Final answer:
The surface temperature of a star with a peak wavelength of 685 nm can be determined using Wien's Displacement Law. The calculated temperature is approximately 4223 Kelvin.
Step-by-step explanation:
The temperature of a star can be determined by using the Wien's Displacement Law which states that the wavelength of the peak emitted radiation is inversely proportional to the temperature of the body. The equation is λmax = b/T, where λmax is the peak wavelength, T is the temperature, and b is the Wien's constant (2.897 x 10⁻³ m.K).
Thus, rearranging the equation, T = b / λmax. Substituting the given peak wavelength (685 x 10⁻⁹ m) and b, T ≈ 4,223 K. So, the surface temperature of the star is approximately 4223 Kelvin.
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