Which of the following lanthanoid does not occur in nature?

Promethium

The correct answer is option 2. Promethium.

The lanthanoid that does not occur in nature is Promethium (Pm). It is the only lanthanoid that is not found in the Earth's crust. All of the other lanthanoids, including cerium, praseodymium, and erbium, are found in the Earth's crust.

Promethium is created in nuclear reactors, and it is also found in the decay products of uranium and thorium. However, it is not found in significant amounts in the Earth's crust.

The reason why promethium does not occur in nature is because it is a very unstable element. Its longest-lived isotope, promethium-147, has a half-life of only 17.7 years. This means that promethium-147 decays very quickly, and it is not able to accumulate in the Earth's crust.

So the answer is 2. Promethium.