The radiation from the source is characterized by a frequency of 4.5 * 10 ^ 14 Hz.

The radiation from the source is characterized by a frequency of 4.5 * 10 ^ 14 Hz. Determine the temperature of this source if its properties are close to a black body.

Let’s write down briefly given:

v = 4.5 * 10 ^ 14 Hz.

To find:

T -?

To solve the problem, we will apply Wien’s displacement law. Let us remember him first of all.

Wien’s law of displacement gives the dependence of the wavelength at which the radiation flux of the energy of a black body reaches its maximum on the temperature of the black body.

In general, we write it down:

λmax = b / T ≈ 0.002898 m * K × T −1 (K),

where T is the temperature and λmax is the wavelength with the maximum intensity. The coefficient b, called Wien’s constant, in SI has a value of 0.002898 m * K.

Let us express T:

T = v * 0.29 * 10 ^ -3 / s = 4.5 * 10 ^ 14 * 0.29 * 10 ^ -3 / 3 * 10 ^ 8 = 435 degrees.