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: Understand the question.
Star P glows yellow and star Q glows blue. We must compare their surface temperatures.

Step 2: Recall Wien's law.
Wien's displacement law says a hot body glows with a shorter peak wavelength. In a formula:
\[ \lambda_m T = b \quad\Rightarrow\quad T \propto \frac{1}{\lambda_m} \]
So a higher temperature goes with a shorter wavelength.

Step 3: Compare the colours.
In the visible spectrum, yellow light has a longer wavelength than blue light. So $\lambda_P$ (yellow) is bigger than $\lambda_Q$ (blue).

Step 4: Apply the inverse rule.
Since temperature is one over the wavelength, the star with the longer wavelength is cooler. The yellow star P has the longer wavelength.

Step 5: Decide the order.
So star P is cooler than star Q, meaning $T_P < T_Q$.

Step 6: Write the answer.
The relation is $T_P < T_Q$. This matches option (4).
\[ \boxed{T_P < T_Q} \]