An intro question about the magnification factor of an SEM

[fatmike6305]

An intro question about the "magnification factor" of an SEM

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 7.0 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?

I calculated that A) is 1.2e-2, but was incorrect. Not sure if it's the notation that I'm using. Also, confused on B.

I'd like to point out that there are absolutely NO example problems of anything similar in the text. Frustrating

 

[jbsteele]

. A) The diameter of the vessel itself is 0.12 cm.B) The cross-sectional area of the vessel has been increased by a factor of 360000 (6002).

 

[thomate1]

I understand your frustration with not having examples to reference for this specific topic. However, I can provide some guidance on how to approach these types of questions.

First, let's define the magnification factor of an SEM. This refers to the ratio between the size of the image produced by the SEM and the actual size of the object being imaged. In this case, the magnification factor is 600, meaning the image is 600 times larger than the actual object.

For part (a), we need to use the magnification factor to calculate the diameter of the vessel. We can set up a proportion:

600 = (diameter of image) / (diameter of vessel)

Solving for the diameter of the vessel, we get:

diameter of vessel = (diameter of image) / 600

Plugging in the given values, we get:

diameter of vessel = 7.0 cm / 600 = 1.2 x 10^-2 cm

So your initial calculation was correct, but it's important to keep track of units and use the correct notation (e.g. using scientific notation for very small numbers).

For part (b), we need to calculate the factor by which the cross-sectional area of the vessel has been increased in the micrograph. This can be done by using the formula for the area of a circle (A= πr^2) and comparing the area of the vessel in the micrograph (A') to the actual area of the vessel (A).

A' = π (diameter of image / 2)^2 = π (3.5 cm)^2 = 38.48 cm^2

A = π (diameter of vessel / 2)^2 = π (1.2 x 10^-2 cm / 2)^2 = 1.13 x 10^-4 cm^2

The factor by which the area has been increased is therefore:

A' / A = (38.48 cm^2) / (1.13 x 10^-4 cm^2) = 3.41 x 10^8

This means that the cross-sectional area of the vessel has been increased by a factor of approximately 3.41 x 10^8 in the micrograph.

I hope this helps clarify the calculations and concept of magnification factor in SEM images. Remember, practice and repetition are key in understanding