A great physicist of this century (P. A. M. Dirac) loved playing with numerical values of fundamental constant of nature. This led him to an instreasing observaion. Dirac found that form the basic constant of atomin physice (c,e, mass of electron mass of proton) and the gravitational constant G, he could arrive at a number with the dimension of time. Further, it was a very large number, its magnitude being close to the present estimate on the age of the universe `(~~ 15 billion years).` Form the table of fundamental constants in this book, try to see if you too can construct this number (or any other instresting number you can think of). if its coincidence with the age of the universe ware significant, what would this imply for the constancy of fundamental constants ?

Explanation

Trying out with basci constants of atomic physics (speed of light c, charge on electron e, mass of electron
`m_e` mass of proton `m_p`) and universal gravitational constant G, we can arrive at a quantity which has the
dimensions of time. Once such quatity si `t = ((e^2)/(4pi "in"_0))^2xx(1)/(m_p m_e^2 c^3G)`
Put `e = 1.6xx10^(-19)C, (1)/(4pi"in"_0) = 9xx10^9, c = 3xx10^8m//s and G = 6.67xx10^(-11) Nm^2kg^(-2)`
`m_p 1.67xx1-^(-27)kg , m_e = 9xx10^(-31)kg`
`t = (1.6xx10^(-19))^4xx(9xx10^9)^2xxx(1)/(1.67xx10^(-27)(9xx10^(-31))^2(3xx10^8)^3xx6.67xx10^(-11))`
`t = 2.18xx10^(16) sec`. This time is of the order of age of universe.