Question

Two stars 'P' and 'Q' emit yellow and blue light respectively. The relation between their temperatures ($T_P$ and $T_Q$) is

• A. $T_P = T_Q$
• B. $T_P = T_Q^2$
• C. $T_P > T_Q$
• D. $T_P < T_Q$

Hint:

Counterintuitively, in astronomy and thermodynamics, "blue hot" is much hotter than "red hot" or "yellow hot". The closer a color is to the violet/ultraviolet end of the spectrum, the hotter the object emitting it.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
We are given the peak emission colors of two stars and must determine the mathematical relationship between their surface temperatures.

Step 2: Key Formula or Approach:
Wien's Displacement Law states that the peak emission wavelength ($\lambda_m$) of a black body is inversely proportional to its absolute surface temperature ($T$).
$$\lambda_m T = b \implies T \propto \frac{1}{\lambda_m}$$

Step 3: Detailed Explanation:
From Wien's Law, a hotter star will emit light with a shorter peak wavelength, and a cooler star will emit light with a longer peak wavelength.
Star P emits yellow light, and Star Q emits blue light.
In the visible light spectrum (VIBGYOR), the wavelength of yellow light ($\lambda_P$) is significantly longer than the wavelength of blue light ($\lambda_Q$).
Since $\lambda_P > \lambda_Q$, the inverse relationship dictates that the temperature of star P must be lower than the temperature of star Q.
Therefore, $T_P < T_Q$.

Step 4: Final Answer:
The relation between their temperatures is $T_P < T_Q$, matching option (D).