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The values of different fundamental constants are given below : <br> `{:("Charge on an electron,",e=1.6xx10^(-19) C),("Mass of an electron,",m_(e)=9.1xx10^(-31) kg),("Mass of a proton",m_(p)=1.67xx10^(-27) kg),("Speed of light",c=3xx10^(8)m//s),("Gravitational constant,",G=6.67xx10^(-11) N m^(2) kg^(-2)):}` <br> `1/(4pi epsi_(0))=9xx10^(9) Nm^(2) C^(-2)` <br> We have to try to make permutations and combination of the universal constants and see if there can be any such combination whose dimensions come out to be the dimensions of time. One such combination is : <br> `(e^(2)/(4 pi epsi_(0)))^(2). (1)/(m_(p) m_(e)^(2)c^(3)G)` <br> According to Coulomb's law of electrostatics, <br> `F=1/(4pi epsi_(0))=((e)(e))/r^(2)` <br> or, `1/(4pi epsi_(0))=(F r^(2))/e^(2)` or `(1/(4 pi epsi_(0)))^(2)=(F^(2)r^(4))/e^(4)` <br> According to Newton's law of gravitation, <br> `F=G (m_(1)m_(2))/r^(2)` or `G=(Fr^(2))/(m_(1)m_(2))` <br> Now, `[e^(4)/((4pi epsi_(0))^(2) m_(p) m_(e)^(2)c^(3)G)]=[e^(4)((F^(2) r^(4))/e^(4))1/(m_(p)m_(e)^(2)c^(3))(m_(1)m_(2))/(Fr^(2))]` <br> `=[(Fr^(2))/(mc^(3))]=[(MLT^(-2)L^(2))/(ML^(3)T^(-3))]=[T]` <br> Clearly, the quantity under discussion has the dimensions of time. Substituting values in the quantity under discussion, we get <br> `((1.6xx10^(-19))^(4)(9xx10^(9))^(2))/((1.69xx10^(-27))(9.1xx10^(-31))^(2)(3xx10^(8))(6.67xx10^(-11)))` <br> `=2.1xx10^(16)` second <br> `= (2.1 xx10^(16))/(60xx60xx24xx365.25)` years <br> `=6.65xx10^(8)` years <br> `=10^(9)` years <br> The estimated time is nearly one billion years.Related Video

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