Question

1 in which order are the objects listed formed during the life cycle of a star? 3 marks
a. protostar > red giant > supernova > stable star
b. protostar > stable star > red supergiant > supernova
c. red giant > stable star > protostar > supernova
d. red giant > supernova > protostar > stable star

2 carbon-14 has a half-life of 5700 years. a 10 g sample of wood cut recently from a living tree has an activity of 160 counts/minute. a piece of charcoal taken from a prehistoric campsite also weighs 10 g but has an activity of 40 counts/minute. estimate the age of the charcoal. 3 marks
a. 11460 years
b. 11400 years
c. 5700 years
d. 17100 years

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3 matter is generally found in one of three phases: solid, liquid, and gas. a substance can be converted from a solid to a liquid and then from a liquid to a gas by adding heat. once the temperature of a solid substance reaches its melting point, any heat added is used to change the solid to the liquid phase. so, while the phase is changing, the temperature of the substance remains constant. once the phase change is complete, the temperature of the liquid continues to rise. similarly, once the temperature of a liquid reaches the boiling point, any heat added is used to change the liquid to the gas phase, and the temperature remains constant while the phase is changing.
at which points are temperature changes occurring in the graph above? 3 marks
temperature and phase changes
of a substance

a. a and e
b. a, c and e
c. b and d

Explanation:

Question 1

Step1: Recall star life cycle

A star starts as a protostar, then becomes a stable (main - sequence) star. After that, for massive stars, it becomes a red supergiant, and finally undergoes a supernova.

Step2: Analyze options

• Option A: Stable star should come before red giant/supergiant, so A is wrong.
• Option B: protostar → stable star → red supergiant → supernova follows the correct life cycle.
• Option C: Protostar is the first stage, so C is wrong.
• Option D: The order is completely reversed, so D is wrong.

Step1: Understand half - life concept

The half - life ($t_{1/2}$) of Carbon - 14 is 5700 years. The activity of a radioactive sample is proportional to the number of radioactive atoms. The formula for the number of half - lives ($n$) is given by the ratio of the initial activity ($A_0$) to the final activity ($A$), where $A=\frac{A_0}{2^n}$.

Step2: Calculate number of half - lives

Given $A_0 = 160$ counts/minute and $A = 40$ counts/minute. So, $\frac{160}{40}=4 = 2^n$. Solving for $n$, we get $n = 2$ (since $2^2=4$).

Step3: Calculate age

The age of the charcoal is $n\times t_{1/2}$. Substituting $n = 2$ and $t_{1/2}=5700$ years, we get age $=2\times5700 = 11400$ years.

Step1: Recall phase change and temperature

During phase changes (melting at B, boiling at D), the temperature remains constant. When the substance is in a single phase (solid at A, liquid at C, gas at E), adding heat increases the temperature.

Step2: Analyze the graph

Points A (solid, temperature rising), C (liquid, temperature rising), and E (gas, temperature rising) are where temperature changes occur. Points B (melting, phase change) and D (boiling, phase change) have constant temperature.

Answer:

B. protostar > stable star > red supergiant > supernova

Question 2