Step 1: Composition of the bulk Earth.
Geochemical studies (including meteorite composition and seismic density models) indicate that the Earth is made primarily of four major elements:
- Iron (Fe)
- Oxygen (O)
- Silicon (Si)
- Magnesium (Mg)
Together these four account for $\sim$90% of Earth's mass.
Step 2: Why Mg?
- In the mantle, the dominant minerals are olivine (Mg,Fe)$_2$SiO$_4$ and pyroxenes (Mg,Fe)SiO$_3$, showing the dominance of Mg.
- The crust contains Al and Ca in feldspars, but their abundance in the whole Earth is much smaller compared to Mg.
- Na is a trace constituent, not a bulk component.
Step 3: Supporting evidence.
The average bulk Earth composition (by weight):
- Fe $\approx 35%$
- O $\approx 30%$
- Si $\approx 15%$
- Mg $\approx 14%$
Other elements (Al, Ca, Na, K, etc.) are present in much smaller amounts.
Final Answer:
\[
\boxed{\text{Mg}}
\]
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The mean of the posterior distribution is (Answer in integer)
Consider a medium of uniform resistivity with a pair of source and sink electrodes separated by a distance \( L \), as shown in the figure. The fraction of the input current \( (I) \) that flows horizontally \( (I_x) \) across the median plane between depths \( z_1 = \frac{L}{2} \) and \( z_2 = \frac{L\sqrt{3}}{2} \), is given by \( \frac{I_x}{I} = \frac{L}{\pi} \int_{z_1}^{z_2} \frac{dz}{(L^2/4 + z^2)} \). The value of \( \frac{I_x}{I} \) is equal to 
Suppose a mountain at location A is in isostatic equilibrium with a column at location B, which is at sea-level, as shown in the figure. The height of the mountain is 4 km and the thickness of the crust at B is 1 km. Given that the densities of crust and mantle are 2700 kg/m\(^3\) and 3300 kg/m\(^3\), respectively, the thickness of the mountain root (r1) is km. (Answer in integer)