Physics spans the very small and the very large

MATHEMATICS · Multi-part · CBSE · Mathematics · Power Play · Power Play

Problem

Physics spans the very small and the very large. Consider the following extreme length scales: • Planck length

\ell_{P}=0.000000000000000000000000000000000016\,\text{m}

• Radius of the observable universe

R_{u}=4.4\times10^{26}\,\text{m}

(i) Write the Planck length in scientific notation with one non-zero digit before the decimal point. (ii) State the order of magnitude of

\ell_{P}

and of

R_{u}

. (iii) Determine the number of orders of magnitude between

\ell_{P}

and

R_{u}

. (iv) Calculate the ratio

\dfrac{R_{u}}{\ell_{P}}

and express the answer as

a\times10^{n}

with

1\le a<10

. (v) On the basis of your result in part (iv), explain briefly what the comparison reveals about the range of length scales encountered in physics.