What is the frequency of an EM wave emitted most strongly by a
glowing element on a stove with temperature 1500 K?
www.wikipedia.org/wiki/Wien's_displacement_law
To determine the frequency of an electromagnetic (EM) wave emitted most strongly by a glowing element on a stove, we can use Wien's displacement law.
Wien's displacement law states that the wavelength of the peak emission from a black body is inversely proportional to its temperature. This can be expressed mathematically as:
λmax = b / T
where λmax is the wavelength of the peak emission, T is the temperature in Kelvin, and b is Wien's displacement constant equal to approximately 2.898 x 10^-3 meters Kelvin.
To find the frequency (f) of the EM wave, we can use the formula:
f = c / λ
where c is the speed of light, approximately 3 x 10^8 meters per second, and λ is the wavelength.
Step 1: Convert the temperature to Kelvin
Given temperature is 1500 K.
Step 2: Calculate the wavelength of the peak emission
Using Wien's displacement law:
λmax = b / T
λmax = 2.898 x 10^-3 / 1500
Step 3: Calculate the frequency
Using the formula:
f = c / λ
f = (3 x 108) / λmax
Let's calculate the values in the next step.
To determine the frequency of an electromagnetic (EM) wave emitted most strongly by a glowing element on a stove with a temperature of 1500 K, we can use Wien's displacement law.
Wien's displacement law states that the wavelength of light emitted by a black body is inversely proportional to its temperature. Mathematically, the law can be expressed as:
λ_max = b / T
where λ_max is the wavelength at which the intensity of radiation is maximum, b is a constant called Wien's displacement constant (approximately 2.898 x 10^-3 m·K), and T is the temperature of the black body in Kelvin.
To find the frequency, we can use the formula:
f = c / λ
where f is the frequency, c is the speed of light (approximately 3.00 x 10^8 m/s), and λ is the wavelength.
Let's calculate the frequency:
1. Convert the temperature from Celsius to Kelvin:
T_K = T_C + 273.15
T_K = 1500 + 273.15 = 1773.15 K
2. Find the wavelength using Wien's displacement law:
λ_max = b / T_K
λ_max = 2.898 x 10^-3 m·K / 1773.15 K
3. Calculate the frequency:
f = c / λ_max
f = 3.00 x 10^8 m/s / λ_max
By performing these calculations, we can determine the frequency of the EM wave emitted most strongly by the glowing element on the stove.