The hottest stars have surface temperatures of about 40,000 K. At what wavelength do they emit the most radiation?
7.2 x 10E-6 cm
2.5 x 10E-4 cm
4.0 x 10E-2 cm
1.2 x 10E2 cm
1.4 x 10E6 cm
aren't short wavelengths the most energetic?
7.2 x 10E-6 cm
To determine at what wavelength the hottest stars emit the most radiation, we can use Wien's displacement law. According to this law, the wavelength at which the radiation intensity is maximum is inversely proportional to the temperature.
The formula to calculate the wavelength of maximum radiation intensity is given by:
λmax = b / T
where λmax is the wavelength, T is the temperature in Kelvin, and b is Wien's constant, which is approximately equal to 2.898 × 10^-3 m·K.
Let's plug in the given temperature of 40,000 K into the formula:
λmax = (2.898 × 10^-3 m·K) / (40,000 K)
Now, we need to convert the wavelength into centimeters. We can do this by multiplying by 100:
λmax = ((2.898 × 10^-3) × 100) / 40,000 cm
Simplifying the expression:
λmax = 7.245 × 10^-6 cm
Comparing this result with the provided options, we can see that the closest value is 7.2 x 10E-6 cm. Therefore, the correct answer is 7.2 x 10E-6 cm.