Determine lamda m Oments wavelength of the peak of the Planck distribution annd the corresponding frequency f at these temperature
a) 3.00k. b)300k c)3000k
https://en.wikipedia.org/wiki/Wien%27s_displacement_law
To determine the wavelength and frequency corresponding to the peak of the Planck distribution at a given temperature, we can use Wien's displacement law. This law states that the wavelength of the peak (lambda_m) is inversely proportional to the temperature (T), and the frequency (f) is directly proportional to the temperature (T).
Wien's displacement law can be expressed as:
lambda_m * T = constant
where the constant is known as Wien's displacement constant (denoted as 'b').
We can substitute the given temperatures into the equation to calculate the corresponding lambda_m and f.
a) For T = 3.00K:
Using Wien's displacement law, we have:
lambda_m * 3.00K = constant
Substituting the value of the constant (b) and rearranging the equation, we can solve for lambda_m:
lambda_m = b / 3.00K
To find the corresponding frequency (f), we can use the relationship between frequency, speed of light (c), and wavelength:
f = c / lambda_m
b) For T = 300K:
Following the same steps as above, we have:
lambda_m * 300K = constant
Solving for lambda_m:
lambda_m = b / 300K
To find f, we use the relationship:
f = c / lambda_m
c) For T = 3000K:
Using the same process, we have:
lambda_m * 3000K = constant
Solving for lambda_m:
lambda_m = b / 3000K
And for f:
f = c / lambda_m
Now, to obtain the exact values for lambda_m and f, we need to know the value of b (Wien's displacement constant). The value of b is approximately 2.898 x 10^-3 m·K (meters Kelvin) or 2.898 x 10^-12 m·K (meters Celsius).