Aplate of the steel hull of a ship develops a large crack when the ship strikes a reef. analysis of the steel’s composition shows higher-than-normal levels of an element that could explain why the plate cracked instead of bending. which element is most likely suspected?
iron
sulfur
chromium
nickel

sulfur

Explanation:

Sulfur is a non-metallic element that is located in family 16, also known as the calcogen family. Its name derives from the Latin “sulfur” and because of that its symbol is S.

Sulfur is found in nature in free form or in compounds such as sulfates and sulfides. It is commonly found in volcanic regions, and is a low hardness metal, which causes it to crack and not to bend when impacted.

For this reason we can say that in the case of the above question the cracked plate was made of sulfur.

part 1: the half-life of the element is 22 years.

part 2: it will take 132.02 year for the sample to decay from 308.0 g to 4.8125 g.

explanation:

part 1: there are two ways to determine the half life time.

first way: the half life time can be determined directly from its definition as it is the time required for the sample to decay to its half concentration.

from the data the initial concentration was 45.0 g and decayed to its half value (22.5 g) in 22.0 years.

second way: the radio active decay is considered first order reaction so we can use the laws of first order reactions.

k = (1/t) ln (a/a-x), where k is the rate constant of the reaction,

t is the time of the reaction

a is the initial concentration of the reactant

a-x is the remaining concentration at time (t)

a = 45.0 g the initial concentration at t = 0 year.

at t = 22 year, a-x = 22.5 g

then k = (1/22 year) ln (45.0 g/ 22.5 g) = 0.0315 year-1.

the half-life time (t1/2) = ln 2/ k = 0.693/ k =0.693/ 0.0315 = 22 years.

part 2:

using the same law k = (1/t) ln (a/a-x),

using the given data; a = 308.0 g and a-x = 4.8125 g and the calculated k from the part 1 (k = 0.0315 year-1)

t = (1/k) ln (a/a-x) = (1/0.0315) ln (308.0/ 4.8125) = 132.02 years