How High Could a Mountain Be?

M.N.Murty

Visiting Faculty, Department of Physics, Sri Sathya Sai Institute of Higher Learning, Prasanthi Nilayam-515134, Andhra Pradesh, India.

Abstract Mount Everest is the world’s highest mountain and it has a height of about 9Km. The estimation of the maximum of height of a mountain on earth using basic physics is done by famous Physicist victor Weisskopf (1908 – 2002). According to Weisskopf, the height of a mountain on earth cannot be more than 44Km. If the height of a mountain is more than this critical value, the mountain would start sinking. During the sinking processes, the directionality of the bonds between the atoms of the solid rock below breaks due to the weight of the mountain. As a result, solid rocks below melt and flow aside. This value was estimated by taking the solid rock below the mountain as SiO2 and the ratio of liquefaction energy to binding energy of the solid rock was supposed to be same as that of ice. Actually, this maximum value of the height of a mountain is less than 44Km because the rock below is warm and needs less energy to liquefy. Weisskopf has also derived a formula in terms of fundamental constants for calculating the critical height of a mountain on any planet with same material structure as earth, if the number of nucleons in the planet is known.