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The radius of the proton is about $10^{- 15} m .$ The radius of the observable universe is $10^{26} m .$ Identify the distance which is half-way between, these two extremes on a logarithmic scale.

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$10^{21} m$

$10^{6} m$

$10^{- 6} m$

$10^{0} m$

answer is B.

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Detailed Solution

$r_{1} = 10^{- 15} m, r_{2} = 10^{26} m$

$\log r = \frac{1}{2} [\log 10^{- 15} + \log 10^{26}]$

$= \frac{1}{2} [- 15 + 26] = 5.5 \approx 6$

$\Rightarrow r = 10^{6} m$

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