Considering that the mantle is 44.8% oxygen and 21.5% silicon by mass, calculate the mole ratio of oxygen atoms to silicon atoms in the mantle.

The mantle has a mass of around that is around 68.4% of earth's mass.

So to calculate moles we need to first find out the mass of oxygen and silicon present in mantle. It is given that oxygen is 44.8% by mass in mantle and 21.5% by mass in mantle, therefore to calculate its mass, we need to use

Now, to calculate mass percentage of oxygen

Similarly the mass of silicon can be calculated

Now, the moles of any substance is calculated by

where, mass of oxygen in kilograms is

So,

Similarly

Now, to calculate mole ratio we need to divide every moles to the lowest calculated mole that is the moles of Si and round it off to the nearest whole number.

The mole ratio of oxygen atoms to silicon atoms in mantle is 3.6 : 1

Explanation:

To calculate the mole ratio of oxygen and silicon in mantle, use will follow some steps:

Step 1: Converting Mass percent into mass of Oxygen and Silicon.

We are given 44.8% of oxygen is present in mantle by mass.

This means that 44.8 grams of oxygen is present in 100 grams of mantle.

Similarly, 21.5 grams of silicon is present in 100 grams of mantle.

Step 2: Calculating the moles of Oxygen and Silicon.

To calculate the number of Moles, we will use the formula:

Molar mass of oxygen = 16 g/mol

Given mass of oxygen = 44.8 grams

Putting values in above equation, we get:

Molar mass of silicon = 28 g/mol

Given mass of silicon = 21.5 grams

Putting values in above equation, we get:

Step 3: Calculating the number of atoms of Oxygen and Silicon.

According to mole concept:

1 mole of an element contains number of atoms.

2.8 moles of oxygen will contain atoms

0.767 moles of silicon will contain atoms

Step 4: Calculating the mole ratio of Oxygen and Silicon atoms

Mole ratio of atoms of Oxygen : Silicon =

Hence, the mole ratio of atoms of Oxygen and Silicon is 3.6 : 1

A) It limits the nuclear spin to certain allowed spin states.

Explanation:

A nucleus with an odd atomic number or an odd mass number has a nuclear spin, which can be observed through NMR.

A proton is the simplest nucleus, and its odd atomic number of 1 implies that it has one spin. We can visualize a spinning proton as a positively charged rotating sphere. This movement of a  charged particle is like an electric current in a wired loop. It generates a magnetic field called the magnetic moment. When a small magnetic bar is placed in the field of a larger magnet, it rotates to align itself with the field of the larger magnet, a lower energy arrangement than an orientation against the field. Quantum mechanics requires that the proton's magnetic moment is aligned with the external field or against the field. The lowest energy state with the proton aligned with the field is called the spin alpha state (α spin).  The higher energy state with the proton aligned against the external magnetic field is called the beta spin state (β spin).

In the absence of an external magnetic field, the magnetic moments of the protons have random orientations. When an external magnetic field is applied, each proton in a sample it assumes β state or α state. Because the state of spin α is lower in energy, there are more α spins than β spins.