Question

Calculate the temperature of the black body if the peaks of the spectrum distribution are in

a) gamma ray= 1.00 x10^-14 m
b) red light= 670 nm
c) x-rays,=1.0 nm,
d) TV waves=1.00 m
e) AM radio waves,= 204 m.

Answer 1

The temperature of a black body can be calculated using Wien's law, which relates the wavelength at which the emission is highest to the temperature of the black body. The formula to find temperature (T) is T = Wein's displacement constant (λmax) / Peak wavelength (λmax). Applying this law to the given wavelengths for gamma rays, red light, x-rays, TV waves, and AM radio waves results in temperatures ranging from billions to tens of Kelvins

Step-by-step explanation:

To calculate the temperature of a black body when given the peak wavelength of its spectrum, we use Wien's law, which states that the peak wavelength (λmax) is inversely proportional to the temperature (T) of the black body. The relationship is given by the formula:

λmax * T = b

where b is Wien's displacement constant, approximately 2.897 x 10-3 m·K, and λmax is the wavelength at which the emission is highest. Thus, the temperature can be found using the equation:

T = b / λmax

1. For gamma rays (λmax = 1.00 x 10-14 m), the temperature (T) is calculated as: T = 2.897 x 10-3 m·K / 1.00 x 10-14 m = 2.897 x 1011 K.
2. For red light (λmax = 670 nm or 670 x 10-9 m), T = 2.897 x 10-3 m·K / 670 x 10-9 m = 4.325 x 106 K.
3. For x-rays (λmax = 1.0 nm or 1.0 x 10-9 m), T = 2.897 x 10-3 m·K / 1.0 x 10-9 m = 2.897 x 106 K.
4. For TV waves (λmax = 1.00 m), T = 2.897 x 10-3 m·K / 1.00 m = 2.897 x 103 K.
5. For AM radio waves (λmax = 204 m), T = 2.897 x 10-3 m·K / 204 m = 14.2 K.