(III) The smallest meaningful measure of length is called the Planck length, and is defined in terms of three fundamental constants in nature: the speed of light c the gravitational constant G = 6.67 × 10-11 m³/kg•s², and Planck's constant h = 6.63 × 10-34 kg·m²/s. The Planck length {p is given by the following combination of these three constants: 3.00 × 10° m/s, Gh lp Show that the dimensions of lp are length [L], and find the order of magnitude of lp. [Recent theories (Chapters 32 and 33) suggest that the smallest particles (quarks, leptons) are “strings" with lengths on the order of the Planck length, 10-35 m. These theories also suggest that the “Big Bang," with which the universe is believed to have begun, started from an initial size on the order of the Planck length.]

We are going to make a simple approximation of the number of atoms in the universe. Assume all the atoms in the universe are hydrogen. (In actual practice, over 75% of the atoms in the universe are hydrogen.) Assume the sun is a typical star (made of pure hydrogen) has a density of 1.4 g/cm3 and is a sphere with a radius of 7.0*108m Assume that there are 100 billion stars in our Milky Way galaxy that are identical to our sun. Assume that there are 10 billion galaxies in the universe identical to our Milky Way galaxy. How many atoms are there in the universe?

I would like to request the solution to be in a line-by-line format instead of being a whole paragraph? Thank you!