The radiation emitted from a star has a maximum intensity at a wavelength of 500 nm. What is the temperature of this star
A)6,000 K
B)5,000 K
C)$1.5 × 10^9$ K
D)500 K
E)10,000 K

Question

Quizplus · Accepted Answer

This question can be solved using Wien's law, which states that the wavelength of maximum intensity emitted by an object is inversely proportional to its temperature. Mathematically, this can be expressed as:

λmax = b/T

where λmax is the wavelength of maximum intensity, T is the temperature, and b is a constant called Wien's displacement constant.

The value of b is approximately equal to 2.898 × 10^-3 mK, so we can rearrange the equation to solve for T:

T = b/λmax

Substituting the given values, we get:

T = 2.898 × 10^-3 mK / 500 nm

T = 5,796 K

Therefore, the temperature of the star is approximately 6,000 K (closest to option A).

The Radiation Emitted from a Star Has a Maximum Intensity 1.5×1091.5 × 10^91.5×109

The Radiation Emitted from a Star Has a Maximum Intensity $1.5 × 10^9$