Question

The table below shows how much of the mass of the Sun and the Earth are made up of each element (by mass). Note that, for this problem, the amounts have been randomized somewhat from their real values. For your answers to this problem, use the values given in the table below. Note that because of rounding, uncertainties in the known values, the applied randomization, and small differences between the solar nebula composition and the composition of the Sun, it is possible to have answers more than 100%.

Element	Percentage by Mass in the Sun	Percentage by Mass in the Earth
Hydrogen	71.1%	0.0033%
Helium	27.4%	2 × 10−8%
Carbon	0.25%	0.045%
Nitrogen	0.08%	0.0004%
Oxygen	0.65%	30.4%
Neon	0.12%	4 × 10−10%
Magnesium	0.07%	13.9%
Silicon	0.06%	16.7%
Sulfur	0.04%	2.9%
Iron	0.14%	32%

Assume that all of the iron in the solar nebula in the Earth's vicinity was incorporated into the Earth. Use the data in the table to calculate what percentages of the available silicon, sulfur, and oxygen were incorporated.

The percentage of silicon is  %.

The percentage of oxygen is  %.

The percentage of sulfur is  %.

Answer 1

Assume that the solar nebula had the same concentration of elements as the sun

This means that a given volume of it contained 0.14% iron.

Suppose that the region in the earth's vicinity had a volume of V.

All the iron particles in this volume resulted in the iron in earth. (32%)

Considering a mass of earth equal to M kg,

The mass of iron, earth got is 0.32*M kg

This much iron was in the volume V. (0.14%)

So, total mass of all substances in V = 0.32*M/0.0014 = 228.57*M kg.

a) amount of silicon in this volume = 228.57*M*0.0006 = 0.137142*M kg

Amount of silicon on earth crust = M*.167 kg

Percentage of silicon earth got = 100*.167/0.137142 = 121.77%

b) amount of oxygen in this volume = 228.57*M*0.0065 = 1.485705*M kg

Amount of oxygen on earth crust = M*.0.304 kg

Percentage of oxygen earth got = 100*0.304/1.485705 = 20.462%

c) amount of sulfur in this volume = 228.57*M*0.0004 = 0.091428*M kg

Amount of sulfur on earth crust = M*.029 kg

Percentage of sulfur earth got = 0.029/0.091428 =31.27%