The Sun and positions of four stars A, B, C and D are plotted on the grid of a Hertzsprung–Russell (HR) diagram. Which star is a white dwarf?
Correct Answer: \( \boxed{\mathrm{A}} \)
A white dwarf has a high surface temperature but a very low luminosity because it has a small radius.
On the HR diagram, temperature increases towards the left and luminosity increases upwards.
Star A is located in the region of high temperature and low luminosity, which is characteristic of white dwarfs.
Hence, the correct answer is \( \boxed{\mathrm{A}} \).
A star is found to have a parallax angle of \(0.25\) arc-seconds. What is the distance to the star in light years?
Correct Answer: \( \boxed{\mathrm{B}} \)
The distance in parsecs is related to the parallax angle by
\(d=\dfrac{1}{p}\)
where \(p\) is measured in arc-seconds.
Given
\(p=0.25\)
Therefore,
\(d=\dfrac{1}{0.25}=4.0\,\mathrm{pc}\)
Using \(1\,\mathrm{pc}\approx3.26\,\mathrm{ly}\),
\(d=4.0\times3.26\)
\(d\approx13\,\mathrm{ly}\)
Hence, the correct answer is \( \boxed{\mathrm{B}} \).
Detailed explanation
The nuclear radius varies with nucleon number \(A\) as:
\[ R = R_0 A^{1/3} \]
Hence the nuclear volume is proportional to:
\[ V \propto R^3 \propto A \]
Since nuclear mass is also proportional to \(A\), the nuclear density:
\[ \rho = \frac{\text{mass}}{\text{volume}} \]
is approximately constant for all nuclei.
✅ Answer: (B)
