(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.]

(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.]

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

(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.]

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