We know that concentration, temperature, medium and catalyst all affect the direction and the rate of the reaction through the Le Chatelier's Principle, where a system tries to relieve stress when stress is being applied. In order to push the equilibrium towards the right, we need to increase volume, decrease temperature, increase concentration of A and B, and decrease the concentrations of C and D. In the choices provided, only roman numeral I provided a correction suggestion. By increasing temperature, the system would want to go to the side that does not produce heat (the left). By increasing the amount of D, it will tend to shift reaction away from the species being added. By decreasing the volume and thus increasing the pressure, the system would want to shift left towards the side with less moles of gas. 

The following will shift the equilibrium to the left:

• decreased volume (increased pressure)
• increased temperature
• decreased amounts of A and B
• increased amounts of D and C

Of the choices, all are correct except for Roman numeral I. Placing the vessel into an ice bath decreases the temperature of the equilibrium, and thus the system would want to shift towards the side that produces heat to replace the heat lost. 

Alpha decay is the loss of a helium atom from the original particle.

The number of protons is reduced by two, and the nuclear mass is reduced by four.

Positron emission is when the nucleus ejects a positron, or positive equivalent of an electron. It is also known as decay.

Beta decay is when the nucleus ejects a beta particle (electron).

Alpha decay is when the nucleus ejects an alpha particle (helium nucleus).

Electron capture is when the nucleus caputres an electron from the inner most shell. This process converts a proton to a neutron.

Finally, gamma decay is when an excited nucleus emits gamma rays. Gamma rays have no mass or charge.

An emission of a positron is also known to be  decay. A positron emission can be viewed as a positron being ejected; therefore, when potassium undergoes a positron emission, the daughter nucleus will be argon (Ar) with the weight of 39.

To understand how the daughter nucleus was determined, create a positron emission reaction with potassium.

This is an example of beta decay because the atomic number increases (from 6 to 7). This means a neutron has decayed into a proton, which occurs by emitting an electron, .

First note that 15g is 1/8 of the original 120-gram mass, so all but 1/8 of these radium nuclei have decayed. By definition, ½ of the nuclei decay during one half-life. So the number of nuclei remaining after n half-lives is . In this case, three half-lives have elapsed since, . The answer is 3 * 1600 = 4800 years.

In alpha decay a helium nucleus, , is emitted. Since the total number of nucleons must be conserved, the atomic number of the parent nucleus must decrease by two, and the mass number must decrease by four. Here, the new atomic number is 90 - 2 = 88, and new mass number is 234 - 4 = 230. 

When a nucleus ejects a beta particle, the element is undergoing beta decay. The ejection of a beta particle is equivalent to the ejection of an electron. When gold ejects an electron, , the product will be .

Gamma radiation is a highly energetic form of radiation, and is the type of radiation emitted when antimatter and matter annhilate each other upon contact.