The coolest star whose peak blackbody wavelength can be observed with the human eye (the exact range of visible light varies from publication to publication, so use 380nm to 750 nm).

2000 K

To determine the coolest star whose peak blackbody wavelength can be observed with the human eye, we need to find a star with a peak wavelength within the range of 380nm to 750nm.

The peak wavelength of a blackbody spectrum can be calculated using Wien's Law, which states that the wavelength of maximum emitted radiation is inversely proportional to the temperature of the object. The formula for Wien's Law is:

λmax = (2.898 × 10^-3 m·K) / T

where λmax is the peak wavelength in meters and T is the temperature in Kelvin.

To find the coolest star within the visible range, we will calculate the peak wavelength for stars with different temperatures and identify the star with the longest wavelength within the specified range.

Let's consider a temperature range starting from the coolest stars up to the point where the peak wavelength exceeds 750nm:

1. Start with the minimum temperature within this range, which is approximately 2,500 Kelvin. Plug this value into Wien's Law:

λmax = (2.898 × 10^-3 m·K) / 2,500 K
λmax ≈ 1.1592 × 10^-6 meters

2. Calculate the corresponding wavelength in nanometers:

λmax ≈ 1.1592 × 10^-6 meters × 10^9 nm/m
λmax ≈ 1,159.2 nm

3. Check if the peak wavelength falls within the visible range of 380nm to 750nm. In this case, the peak wavelength of the star at 2,500 Kelvin does not fall within the specified range.

4. Increase the temperature to the next value and repeat the calculations until we find a star with a peak wavelength in the visible range.

By repeating this process, we find that the coolest star whose peak blackbody wavelength falls within the range of 380nm to 750nm is approximately 3,900 Kelvin. At this temperature, the peak wavelength is around 744nm, which is just at the upper limit of the visible range.

Therefore, a star with a temperature of approximately 3,900 Kelvin would be the coolest star whose peak blackbody wavelength can be observed with the human eye.

To determine the coolest star whose peak blackbody wavelength falls within the range of visible light (380nm to 750nm), we need to consider the concept of stellar classification and the relationship between temperature and the peak wavelength of blackbody radiation.

Stars are classified based on their temperature, with the widely-used spectral classification system consisting of seven main types: O, B, A, F, G, K, and M. The O-type stars are the hottest, while the M-type stars are the coolest.

The concept of blackbody radiation explains that objects emit electromagnetic radiation over a range of wavelengths, and the peak wavelength of this radiation is dependent on the temperature of the object. According to Wien's displacement law, the peak wavelength (λ_max) is inversely proportional to the temperature (T) of the blackbody.

λ_max = (2.9 * 10^6 nm * K) / T

By rearranging this equation, we can determine the maximum temperature (T_max) at which a star will have its peak blackbody wavelength within the range of visible light.

T_max = (2.9 * 10^6 nm * K) / 380 nm

Plugging the values into the equation, we find:

T_max = 7631 K

Therefore, the coolest star whose peak blackbody wavelength falls within the visible light range is around 7631 Kelvin. This temperature generally corresponds to a K-type star, specifically the cooler K-type stars.

It's important to note that this calculation provides a general estimation based on the assumptions of blackbody radiation, and the exact range of visible light can vary slightly between different sources. Additionally, there might be specific stars within this temperature range that suit the criteria, but further research and observations are required to identify them.