What is the frequency of the EM wave emitted most strongly by a glowing element on a stove with temperature 1,500 K
Ah, the melodious symphony of a stove element! Well, the frequency of the electromagnetic (EM) wave emitted most strongly by a glowing element on a stove can be determined using Planck's law and Wien's displacement law. However, instead of throwing fancy formulas at you, I thought I'd tickle your funny bone with a little analogy: It's like asking how often a funky disco ball at a sizzling temperature of 1,500 K busts out its dazzling moves on the dance floor! Well, the frequency of this "light dance" would be around 2 × 10^14 hertz. So, let's just say it's pretty "hot" on the electromagnetic dancefloor!
To determine the frequency of the electromagnetic (EM) wave emitted most strongly by a glowing element on a stove with a temperature of 1,500 K, we can use Wien's Law.
Wien's Law states that the wavelength (λ) of the radiation emitted by a blackbody is inversely proportional to its temperature (T). Mathematically, the relationship is given as:
λ = b / T
Where:
λ is the wavelength of the radiation
b is Wien's displacement constant, approximately equal to 2.898 × 10^-3 meters kelvin (m·K)
T is the temperature in kelvin (K)
To find the frequency (ν) of the radiation, we can use the speed of light equation:
c = νλ
Where:
c is the speed of light, approximately equal to 3.00 × 10^8 meters per second (m/s)
ν is the frequency of the radiation
Step 1: Calculate the wavelength (λ)
λ = b / T
= (2.898 × 10^-3 m·K) / (1500 K)
≈ 1.93 × 10^-6 meters (m) or 1930 nanometers (nm)
Step 2: Calculate the frequency (ν)
c = νλ
ν = c / λ
= (3.00 × 10^8 m/s) / (1.93 × 10^-6 m)
≈ 1.55 × 10^14 Hertz (Hz)
Therefore, the frequency of the EM wave emitted most strongly by the glowing element on a stove with a temperature of 1,500 K is approximately 1.55 × 10^14 Hz.
To determine the frequency of the electromagnetic (EM) wave emitted most strongly by a glowing element on a stove with a temperature of 1,500 K, we can use Wien's displacement law.
Wien's displacement law states that the peak wavelength (λ) of the radiation emitted by a black body is inversely proportional to its temperature (T). Mathematically, it can be expressed as:
λ = b / T
Where λ is the peak wavelength, b is Wien's displacement constant (approximately 2.898 x 10^-3 m·K), and T is the temperature in Kelvin.
To find the frequency (f) corresponding to the peak wavelength, we can use the formula:
f = c / λ
Where f is the frequency, c is the speed of light (approximately 3 x 10^8 m/s), and λ is the wavelength.
Let's plug in the given temperature of 1,500 K into Wien's displacement law:
λ = (2.898 x 10^-3 m·K) / 1500 K
Calculating this expression, we find that the peak wavelength (λ) is approximately 1.932 x 10^-6 meters.
Now, using the wavelength we found, we can calculate the frequency:
f = (3 x 10^8 m/s) / (1.932 x 10^-6 m)
Evaluating this expression, we find that the frequency (f) is approximately 1.551 x 10^14 Hz, or 155.1 terahertz (THz).
Therefore, the EM wave emitted most strongly by the glowing element on the stove with a temperature of 1,500 K has a frequency of approximately 155.1 THz.