Q. 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.
A) $10^{21}$m
B) $10^{6}$m
C) $10^{- 6}$m
D) $10^{0}$m
Explanation
$r_{1} = 10^{- 15}m,\ r_{2} = 10^{26}$m Log $r = \frac{1}{2}\lbrack\log 10^{- 15} + log10^{26}\rbrack$ =$\frac{1}{2}\lbrack - 15 + 26\rbrack = 5.5 \approx 6 \Rightarrow r = 10^{6}$m
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.