The Planck length is the distance at which classical gravitythe familiar structure of spacetimeis expected to break down due to the interplay of relativity and quantum effects. As a fundamental length scale, the Planck length should depend on fundamental constants related to gravity, relativity, and quantum mechanics: the universal gravitational constant G, the speed of light in vacuum c, and Planck's constant h. Values and units for these quantities can be found in Appendix F at the back of your textbook. [NOTE: These derived units can be expressed in terms of fundamental units: 1 newton 1 N = 1 kgm/s2, 1 joule 1 J = 1 kgm2/s2.] (a) Show how to construct a length expression algebraically by multiplying and dividing appropriate powers of these fundamental constants. [HINT: Start with an expression Gacbhd, and require that it have the MKS dimensions of length. Then solve for exponents a, b, d.] (b) Assuming that this result represents the Planck length as described above, what is its numerical value? How does it compare with conventional distances we might encounter everyday or in our scientific laboratories where atoms and subatomic particles are studied? Is this a length scale that might be physically accessible? [HINT: Be sure to complete your calculation yourself. Simply looking up a value online invariably finds a different result that we get here.]