Huge fluxes of X-rays are detected from the direction of Cygnus X-1 with a spectrum that looks similar to that of a blackbody with a peak wavelength of 1.45 nm (1 nm = 10^-9 m). These X-rays are probably emitted by matter being heated as it falls into a black hole. What is the temperature of this gas? A) 2 * 10⁶ K B) 4205 K C) 2 * 10^-2 K D) 2* 10⁴ K

Question

Quizplus · Accepted Answer

The temperature of the gas can be calculated using Wien's displacement law, which relates the peak wavelength of blackbody radiation to the temperature of the emitting body. The formula is $\lambda_{max} = \frac{b}{T}$, where $b$ is Wien's displacement constant ($2.898 \times 10^{-3} m \cdot K$), $\lambda_{max}$ is the peak wavelength (1.45 nm or $1.45 \times 10^{-9} m$), and $T$ is the temperature in Kelvin. Rearranging for $T$, we get $T = \frac{b}{\lambda_{max}}$. Substituting the given values, we find the temperature to be in the order of $10^{7}$ K, which corresponds to choice A.

Huge Fluxes of X-Rays Are Detected from the Direction of Cygnus