Question

A great physicist of the century (P.A.M. Dirac) loved playing with numerical values of Fundamental constants of nature. This led him to an interesting observation. Dirac found that from the basic constants of nature. This led him to an interesting observation. Dirac found that from the basic constants of atomic physics (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). From the table of fundamental constants, try to see if you too can construct this number (or any other interesting number you can think of). If it's coincidence with the age of universe were significant, what would this imply for the constancy of fundamental constants?

Answer 1

Hii dear,

# Answer- 6 billion years

# Gathered data-
e = 1.6×10^–19 C
mp = 1.67×10^–27 kg
me = 9.1×10^–31 kg
c = 3×10^8 m/s
G = 6.67×10^11 Nm^2/kg^2
1/4πε0 = 9×10^9 Nm^2/C^2

# Explaination-
The age of the Universe in terms of fundamental constants is given by formula-
t = [e^2/(4π.ε0)]^2 × [1 / mp.me^2.c^3.G]

Substituting all values in the equation, we get
t = (1.6×10^-19)^4 × (9× 10^9)^2 / [(9.1×10^-31)^2 × (1.67×10^-27) × (3×10^8)^3 × (6.67×10^-11)]
≈ 6X10^9 years
≈ 6 billion years.

Age of the universe is approx 6 billion years...

Answer 2

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