Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 1 - Introduction, Measurement, Estimating - Problems - Page 19: 39

Answer

The dimensions of $l_p$ are [L]. $l_p \approx 10^{-35} ~m$

Work Step by Step

The dimensions of $l_p$ are $\sqrt{\frac{[L]^3\times[M]\times[L]^2\times[T]^3}{[M]\times[T]^2\times[T]\times[L]^3}}=\sqrt{[L]^2} = [L]$ $l_p = \sqrt{\frac{Gh}{c^3}} = \sqrt{\frac{(6.67\times10^{-11})(6.63\times10^{-34})}{(3.00\times10^8)^3}} = \sqrt{1.64\times10^{-69}}= 4.05\times10^{-35} ~m \approx 10^{-35}~m$
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