ANS:B - 0.2 to 0.4

The maximum change in the hardness of martensite occurs in the carbon content range of 0.2 to 0.4 percent in steel. Martensite is a hard, brittle phase of steel that forms when austenite (the high-temperature phase) is rapidly quenched. The hardness of martensite is strongly influenced by the carbon content of the steel. In the carbon content range of 0.2 to 0.4 percent, the hardness of martensite is maximized. This range is often referred to as the eutectoid composition, where the steel undergoes a phase transformation from austenite to a mixture of ferrite and cementite during cooling, resulting in the formation of a predominantly martensitic microstructure upon quenching. Higher carbon contents can lead to the formation of excess carbides, which can reduce the hardness of martensite due to carbide precipitation. Similarly, lower carbon contents may result in incomplete transformation to martensite, leading to lower hardness. Therefore, the correct answer is 0.2 to 0.4 percent.