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Chapter 1: Problem 11

Length of Galaxies is in order of .......... (a) \(10^{26} \mathrm{~m}\) (b) \(10^{36} \mathrm{~m}\) (c) \(10^{28} \mathrm{~m}\) (d) \(10^{-14} \mathrm{~m}\)

Short Answer

Expert verified
The most appropriate order of magnitude for the length of galaxies is \(10^{26} \mathrm{~m}\) (option a).

Step by step solution

01

Understanding the concept of order of magnitude

Order of magnitude is a way to represent the approximate size of a number, by using the powers of 10. A number's order of magnitude represents the scale it belongs to.
02

Comparing the given options to known galaxy sizes

The sizes of galaxies generally range from a few thousand to over a hundred thousand light years in diameter. In order to compare the given options, we should convert the distance in light years to meters. One light year is approximately \(9.461 \times 10^{15} \mathrm{~m}\).
03

Evaluating option (a) - \(10^{26} \mathrm{~m}\)

Converting this size to light years, we get \(\frac{10^{26}\mathrm{~m}}{9.461 \times 10^{15} \mathrm{~m / light\,year}} \approx 10^{10} \mathrm{~light\,years}\), which is on the higher end of galaxy sizes but still considered plausible.
04

Evaluating option (b) - \(10^{36} \mathrm{~m}\)

Converting this size to light years, we get \(\frac{10^{36}\mathrm{~m}}{9.461 \times 10^{15} \mathrm{~m / light\,year}} \approx 1.057 \times 10^{20} \mathrm{~light\,years}\). This value is far larger than known galaxy sizes and is not considered plausible.
05

Evaluating option (c) - \(10^{28} \mathrm{~m}\)

Converting this size to light years, we get \(\frac{10^{28}\mathrm{~m}}{9.461 \times 10^{15} \mathrm{~m / light\,year}} \approx 10^{12} \mathrm{~light\,years}\). This value is significantly larger than known galaxy sizes and is not considered plausible.
06

Evaluating option (d) - \(10^{-14} \mathrm{~m}\)

Converting this size to light years, we find that \(10^{-14} \mathrm{~m}\approx 10^{-29}\mathrm{~light\,years}\), which is much smaller size compared to the known size of galaxies and is not considered plausible.
07

Concluding the correct option

Based on our evaluation of the given options, we can conclude that option (a) \(10^{26} \mathrm{~m}\) is the most appropriate order of magnitude for the length of galaxies in this context.

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