Q. 163.5( 6 Votes )

If Planck’s const A. Mass of electron (me)

B. Universal gravitational constant (G)

C. Charge of electron (e)

D. Mass of proton (mp )

Answer :

According to plank, the energy of photon is given by the expression,



Where,


f= frequency of light


h= Planck’s constant



Dimension of E=


Dimension of f=


So, dimension of h,




As we can see in the question, we have to relate M, L and T in terms of h and c as fundamental quantities.


There is no charge or ampere dimension so option (c) is eliminated.


We have to check for option a, b and d.


Dimensions of me, mp and G are , and respectively.


For me and mp,


For mass, let


m


By substituting the dimension for each quantity



Now using principal of homogeneity, which states that the dimensions on both sides of a dimensional equation is same, we get



=


Equating like terms and solving above we get,


a+b=1, 2b+c=0, -b-c=0


a=1, b=0, c=0


Substituting the values in equation,


m


m=me


Similarly for length,


l



=


Solving we get,



and for time,



This holds true for both me and mp.


And similarly for G,


Also we know,


Dimension of G=


Let,


m ...........(1)


By substituting the dimension for each quantity



Now using principal of homogeneity, which states that the dimensions on both sides of a dimensional equation is same, we get



=


Equating like terms and solving above we get,


a-c=1, 2a+b+3c=0, -a-b-2c=0


a=1/2, b=1/2, c=-1/2


Substituting the values in equation,


m



Similarly for length and time,


and

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