The peak wavelength and observed color of a 50,000 K star is 58nm and too blue to see with the human eye. True or False.
http://www.jiskha.com/display.cgi?id=1392230927
ultraviolet is not visible for humans.
false
To determine whether the statement is true or false, we need to understand the relationship between temperature and the color of a star. The color of a star is directly related to its temperature.
According to Wien's displacement law, the peak wavelength (λmax) of the radiation emitted by a star is inversely proportional to its temperature. The formula is:
λmax = (b / T),
where λmax is the peak wavelength, T is the temperature, and b is Wien's constant.
If we substitute the given temperature of 50,000 K into the equation, we'd get:
λmax = (b / 50,000 K).
However, we are also given that the peak wavelength is 58 nm, which is 58 × 10^(-9) meters. So we can rewrite the equation as:
58 × 10^(-9) m = (b / 50,000 K).
By rearranging the equation, we find:
b = 2.9 × 10^(-3) m * K.
Now, let's determine the color of the star. The observed color of a star can be estimated using the following approximate ranges:
- Blue stars have peak wavelengths around 400-485 nm.
- Green stars have peak wavelengths around 500-565 nm.
- Yellow stars have peak wavelengths around 570-590 nm.
- Orange stars have peak wavelengths around 595-620 nm.
- Red stars have peak wavelengths around 630-780 nm.
Given that the peak wavelength (λmax) of the 50,000 K star is 58 nm, we can conclude that the statement is False. The observed color of the star would be in the ultraviolet range rather than blue, and it would be too short a wavelength to be visible to the human eye.