The SI unit of thermal conductivity is defined as the amount of heat that can conduct through a material per unit time, per unit area, per unit temperature difference.

Let`s dissect each option to understand their units:

Option 1: Wm `K-1

The unit of this option is watts per meter per degree Celsius. It represents the thermal conductivity of a material. This is the correct answer.

Option 2: Wm/K

The unit of this option is watts per meter per kelvin. It is similar to Option 1, but it uses kelvin instead of degrees Celsius. However, both options are equivalent and can be used interchangeably.

Option 3: Wm-`/K’1

This unit is not a valid SI unit. It is a combination of invalid symbols. Therefore, this option is incorrect.

Option 4: Js-`m ’K

The unit of this option is energy per unit area per unit temperature per unit time, which is not the unit of thermal conductivity. Therefore, this option is incorrect.

In conclusion, the SI unit of thermal conductivity is Option 1: Wm `K-1.