The numbers you mentioned are indeed quite large, but they are based on estimations and theoretical calculations. Let's break it down to provide some perspective.
The estimate of 1.3 x 10^50 atoms in the world is an approximation based on calculations considering the total mass of the Earth, its composition, and the known abundance of elements. It takes into account the vast number of atoms present in the Earth's crust, atmosphere, oceans, and all living organisms combined. However, it's important to note that this estimation can vary depending on the assumptions and methods used in the calculation.
On the other hand, the estimate of 10^21 atoms in a drop of water is based on the assumption that a typical drop of water contains about 0.05 milliliters and that each milliliter of water contains approximately 3.34 x 10^22 water molecules (H2O). Since each water molecule consists of three atoms (two hydrogen and one oxygen), we can estimate that there are roughly 10^21 atoms in a drop of water.
While the difference between these two numbers is indeed significant, it's important to consider the vastness and scale of the natural world. The Earth is an enormous planet with a vast amount of matter and a tremendous number of atoms. It's not surprising to have such large numbers when considering the billions of years of Earth's existence and the countless processes that have shaped it.
So, while the numbers may seem staggering, they are based on scientific estimates and serve as a way to grasp the immense scale of atoms and matter in the world around us.