question_answer

The radius of a proton is about \[\text{1}{{0}^{-\text{9}}}\] micron and the radius of universe is about\[\text{1}{{0}^{\text{28}}}\text{cm}\]. Name a physical object whose size is approximately half way between these two extremes on a logarithmic scale?

Answer:

Here, radius of proton,               \[{{\text{y}}_{\text{1}}}=\text{ 1}{{0}^{-\text{9}}}\text{micron }=\text{1}{{0}^{-\text{15}}}\text{m}\] . and radius of universe,                    \[{{\text{y}}_{\text{2}}}=\text{1}{{0}^{\text{28}}}\text{cm }=\text{ 1}{{0}^{\text{26}}}\text{m}\]  The size y, half way between these two on a logarithmic scale is \[\text{log y }=\frac{\log {{y}_{1}}+\log {{y}_{2}}}{2}=\frac{\log {{10}^{-15}}+\log {{10}^{26}}}{2}=\frac{-15+26}{2}=\frac{11}{2}=5.5\approx 6\]                                                                                                       \[\therefore\]                                                                     \[\text{y}=\text{ 1}{{0}^{\text{6}}}\text{metre}\] This is the order of size of earth. Hence the physical object is earth.