Question

White dwarfs radiate most strongly in the ultraviolet, with a peak wavelength of perhaps 300 nm. What would be the surface temperature of a white dwarf?

A) 12,600 K
B) 9700 K
C) 7800 K
D) 3500 K

Answer 1

Using Wien's Law and the given peak wavelength of 300 nm, we can calculate the surface temperature of a white dwarf to be approximately 9700 K, which matches closest with option B) 9700 K.

Step-by-step explanation:

To determine the surface temperature of a white dwarf based on its peak wavelength, we can use Wien's Law. Wien's Law gives a relationship between the temperature of a star and the wavelength at which it emits the most energy. The formula for Wien's Law can be expressed as λ_max * T = b, where λ_max is the peak wavelength, T is the temperature in Kelvin, and b is Wien's displacement constant, approximately equal to 2.897 x 10^(-3) meter*Kelvin.

Given the peak wavelength λ_max of 300 nm (or 300 x 10^(-9) meters) for the white dwarf, we can rearrange Wien's Law to solve for the temperature (T):

T = b / λ_max

Substituting the known values,

T = (2.897 x 10^(-3) m*K) / (300 x 10^(-9) m)

T = 9,656.67 K

Looking at the choices provided, the surface temperature of the white dwarf that most closely matches our calculation is option B) 9700 K.