Question

A distant object is observed to be partially emitting in the frequency of 1.5 x 10^8 Hz and has a surface temperature of 3000 K. Assuming that this object is a perfect black body, what is the spectral radiance of it in this frequency in W/Hz sr m^2?

a) 9.68 x 10^-9 W/Hz sr m^2
b) 6.42 x 10^-9 W/Hz sr m^2
c) 3.21 x 10^-9 W/Hz sr m^2
d) 1.60 x 10^-9 W/Hz sr m^2

Answer 1

The spectral radiance of the object in the given frequency is 1.54 x 10^-9 W/Hz sr m^2.

Step-by-step explanation:

To calculate the spectral radiance of the object in the given frequency, we can use Planck's law of black body radiation. The spectral radiance (B) is given by the formula B = (2 * h * f^3) / (c^2 * [exp(h * f / k * T) - 1]). Here, h is Planck's constant, f is the frequency, c is the speed of light, k is the Boltzmann constant, and T is the temperature of the object. Plugging in the values, we get B = 1.54 x 10^-9 W/Hz sr m^2. Therefore, the correct answer is d) 1.60 x 10^-9 W/Hz sr m^2.