What is the surface temperature in kelvins of a star that has a peak wavelength of 290 nm?
To determine the surface temperature of a star, we can use Wien's displacement law.
According to Wien's displacement law, the peak wavelength (λ) of the electromagnetic radiation emitted by a black body is inversely proportional to its temperature (T):
λ * T = constant
The constant is known as Wien's displacement constant and has a value of approximately 2.898 x 10^6 nm K.
Now we can rearrange the equation to solve for the temperature:
T = constant / λ
Substituting the given peak wavelength of 290 nm:
T = (2.898 x 10^6 nm K) / (290 nm)
T = 10,003 K
Therefore, the surface temperature of the star is approximately 10,003 Kelvin.
To determine the surface temperature of a star with a peak wavelength of 290 nm, we can use Wien's displacement law. This law states that the peak wavelength (λ) and temperature (T) of a black body radiation are inversely proportional.
Wien's Displacement Law: λ * T = constant
First, we need to convert the given peak wavelength to meters:
λ = 290 nm = 290 × 10^(-9) m
Next, we can rearrange the equation to solve for the temperature:
T = constant / λ
Now, we need to find the constant value. The constant is known as Wien's constant and is equal to approximately 2.898 × 10^(-3) m·K.
Substituting the values into the equation:
T = 2.898 × 10^(-3) m·K / 290 × 10^(-9) m
Simplifying:
T = (2.898 × 10^(-3)) / (290 × 10^(-9)) K
T = 9.993 K
Therefore, the surface temperature of the star is approximately 9.993 Kelvin (K).
To determine the surface temperature of a star, we can use Wien's displacement law, which relates the peak wavelength of the radiation emitted by a black body to its temperature. The law can be expressed as:
λ_max = (b / T),
where λ_max is the peak wavelength, b is the Wien's displacement constant (approximately 2.898 × 10^−3 m·K), and T is the temperature in kelvins.
To find the temperature in kelvins, we need to rearrange the equation:
T = b / λ_max.
Given that the peak wavelength is 290 nm (or 290 × 10^−9 m), we can substitute the values into the equation to find the temperature:
T = (2.898 × 10^−3 m·K) / (290 × 10^−9 m).
By canceling out the units of meters, we can simplify the equation:
T ≈ 10000 K.
Therefore, the surface temperature of the star is approximately 10000 kelvins.