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Chapter 1: Problem 60

A scanning electron micrograph of xylem vessels in a corn root shows the vessels magnified by a factor of \(600 .\) In the micrograph the xylem vessel is \(3.0 \mathrm{cm}\) in diameter. (a) What is the diameter of the vessel itself? (b) By what factor has the cross-sectional area of the vessel been increased in the micrograph?

Short Answer

Expert verified
Answer: The diameter of the actual xylem vessel is 0.005 cm, and the cross-sectional area of the vessel has been increased by a factor of 360,000 in the micrograph.

Step by step solution

01

Calculate the actual diameter of the xylem vessel

To do this, we can use the magnification factor and the diameter of the micrograph. The magnification factor is the ratio of the size in the micrograph to the actual size. Magnification factor = \(\frac{\text{Diameter in Micrograph}}{\text{Actual Diameter}}\) We are given the magnification factor \( = 600\) and the diameter in the micrograph \(= 3.0 \text{cm}\). We can now solve for the actual diameter: Actual Diameter = \(\frac{\text{Diameter in Micrograph}}{\text{Magnification Factor}}\) Actual Diameter = \(\frac{3.0 \text{cm}}{600} = 0.005 \text{cm}\)
02

Calculate the squared magnification factor

Since we are interested in comparing the cross-sectional areas of the actual and magnified vessels, which are proportional to the square of the diameters, we need to calculate the squared magnification factor. I.e., we need to find the factor by which the cross-sectional area has been increased. Let's square the magnification factor of \(600\): Squared Magnification Factor = \((\text{Magnification Factor})^2 = 600^2 = 360,000\)
03

Conclusion

In conclusion, (a) the diameter of the actual xylem vessel is \(0.005 \text{cm}\), and (b) the cross-sectional area of the vessel has been increased by a factor of \(360,000\) in the micrograph.

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