Table 2 summarises some of the properties of four stars in the constellation Hercules - AQA - A-Level Physics - Question 3 - 2017 - Paper 4

To deduce which star is larger between Korophoros and Rutilicus, we need to examine their properties. The star that is of spectral class O tends to be the largest, while the spectral class G (Korophoros) indicates a medium-sized star. Rutilicus is classified as a B-type star, which can also be larger than G-type stars. Given Rutilicus's spectral classification, it is generally inferred to be larger than Korophoros.

To find the corresponding temperature for a black-body radiation curve peaking at a wavelength of 1.0 μm, we use Wien's Displacement Law, which states: $ext{T} = \frac{b}{\lambda_{max}}$ where (b) is a constant approximately equal to 2898 μm·K. Substituting in this equation: $ext{T} = \frac{2898}{1.0} = 2898 \,\text{K}$.

The star that produces the black-body radiation curve peaking at 1.0 μm is likely Rasalgethi, as it is a M-type star. M-type stars have cooler temperatures compared to other spectral classes and have their peak emissions in the infrared spectrum, tending towards longer wavelengths. Thus, a peak at 1.0 μm aligns with the characteristics of an M-type star.

To determine which star has the brightest absolute magnitude, we examine the apparent magnitudes in conjunction with their distances. Rutilicus has the lowest apparent magnitude at 2.1, suggesting it could be the brightest when factoring in distance. Therefore:

• Rutilicus ✓

The absolute magnitude can be calculated using the formula: $M = m - 5 \cdot (\log_{10}(d) - 1)$ Where (M) is the absolute magnitude, (m) is the apparent magnitude, and (d) is the distance in parsecs. For Sarin:

• Apparent magnitude (m) = 3.1
• Distance (d) = 23 pc

Substituting into the formula: $M = 3.1 - 5 \cdot (\log_{10}(23) - 1)$ Calculating (\log_{10}(23) \approx 1.362), we find: $M = 3.1 - 5 \cdot (1.362 - 1) \approx 3.1 - 5 \cdot 0.362 \approx 3.1 - 1.81 \approx 1.29$ Thus, the absolute magnitude of Sarin is approximately 1.29.