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Physics: Space and Astrophysics - Life Cycles of Stars, the Big Bang, and Stellar Nucleosynthesis

Grade 8IB

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Nebula and Protostars: Stars begin as a giant cloud of dust and gas called a nebula. Gravity pulls this matter together to form a protostar. As the core temperature reaches approximately 1.5×107 K1.5 \times 10^7 \text{ K}, nuclear fusion begins.

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Main Sequence Stars: In this stage, the star is in Hydrostatic Equilibrium, where the inward pull of gravity is perfectly balanced by the outward thermal pressure from nuclear fusion. The primary reaction is the fusion of Hydrogen into Helium: 4 11H→ 24He+2e++2νe+energy4 \ ^{1}_{1}H \rightarrow \ ^{4}_{2}He + 2e^{+} + 2\nu_{e} + \text{energy}

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Stellar Nucleosynthesis: Stars are 'element factories'. Small stars fuse Hydrogen into Helium. Massive stars continue to fuse heavier elements like Carbon, Neon, Oxygen, and Silicon until they reach Iron (56Fe^{56}Fe). Elements heavier than Iron are formed during Supernova explosions.

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Life Cycle of Stars: The fate depends on mass. Low mass stars (M<8M⊙M < 8M_{\odot}) become Red Giants, then shed outer layers to leave a White Dwarf. High mass stars (M>8M⊙M > 8M_{\odot}) become Red Supergiants, explode as a Supernova, and leave behind a Neutron Star or a Black Hole.

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The Big Bang Theory: The universe originated from a singularity approximately 13.813.8 billion years ago and has been expanding ever since. Key evidence includes Cosmic Microwave Background Radiation (CMBR) and Redshift of distant galaxies.

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Redshift (zz): When a light source moves away from an observer, its wavelength increases (shifts toward the red end of the spectrum). This is a version of the Doppler Effect applied to light: z=λobserved−λemittedλemittedz = \frac{\lambda_{observed} - \lambda_{emitted}}{\lambda_{emitted}}

📐Formulae

z=Δλλ0z = \frac{\Delta \lambda}{\lambda_{0}}

v=H0×dv = H_{0} \times d

E=mc2E = mc^2

λmax=bT\lambda_{max} = \frac{b}{T}

💡Examples

Problem 1:

A specific absorption line of Hydrogen is measured in a laboratory to be λ0=656 nm\lambda_{0} = 656 \text{ nm}. When observing a distant galaxy, the same line is measured at λ=682 nm\lambda = 682 \text{ nm}. Calculate the redshift (zz) of this galaxy.

Solution:

z=682 nm−656 nm656 nmz = \frac{682 \text{ nm} - 656 \text{ nm}}{656 \text{ nm}}

z=26656z = \frac{26}{656}

z≈0.0396z \approx 0.0396

Explanation:

To find the redshift, we calculate the change in wavelength (Δλ\Delta \lambda) and divide it by the original (rest) wavelength. A positive value for zz indicates the galaxy is moving away from us.

Problem 2:

Calculate the difference in mass if a fusion process converts 1000 kg1000 \text{ kg} of Hydrogen into 993 kg993 \text{ kg} of Helium, and use it to explain where the energy comes from.

Solution:

1000 kg−993 kg7 kg\begin{array}{r} 1000 \text{ kg} \\ - 993 \text{ kg} \\ \hline 7 \text{ kg} \end{array}

The energy released is calculated using E=mc2E = mc^2, where m=7 kgm = 7 \text{ kg}.

Explanation:

The 'missing mass' (7 kg7 \text{ kg}) is converted into energy. Since the speed of light (c≈3×108 m/sc \approx 3 \times 10^8 \text{ m/s}) is very large, even a small mass defect results in a massive energy output, powering the star.