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I was reading my school textbook in which the following statement was given:

The resolution of such an electron microscope is limited finally by the fact that electrons can also behave as waves! (You will learn more about this in class XII). The wavelength of an electron can be as small as a fraction of an angstrom.

What does the highlighted statement mean?

Does it mean $1 \:\mathrm{angstrom}/100$?

Or $1\:\mathrm{angstrom}/1\:\mathrm{angstrom}$?

Basically, I just want to know how will the above statement can be represented mathematically?

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    $\begingroup$ This appears to be less a question about physics and more about the English language: "as small as a fraction of an X" means effectively the same as "smaller than an X". $\endgroup$
    – ACuriousMind ♦
    Commented Aug 25, 2018 at 11:02
  • $\begingroup$ How will write it mathematically? 10^-20 angstrom? $\endgroup$
    – Saksham Sharma
    Commented Aug 25, 2018 at 11:04
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    $\begingroup$ It is spelled ångström. $\endgroup$
    – Qmechanic ♦
    Commented Aug 25, 2018 at 11:09
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    $\begingroup$ @SakshamSharma Well, you'd write it as $10^{-20} Å$ and it is certainly is a fraction of an angstrom. And no, "1 Angstrom/1Angstrom" doesn't make any sense. $\endgroup$
    – user199113
    Commented Aug 25, 2018 at 11:10
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    $\begingroup$ Related: english.stackexchange.com/q/231311 $\endgroup$
    – jinawee
    Commented Aug 25, 2018 at 14:38

2 Answers 2

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This construction is a slightly fuzzy use of the English language, and it does not have any specific, definite meaning.

In essence, what it's conveying is that the wavelength $\lambda$ in question can be smaller than 1 angstrom, $$ \lambda < 1 \: Å. $$ However, it does not really specify how much smaller that wavelength will be. Typically you'd use that language for situations in which $\lambda \approx 0.1 \: Å$ is achievable, going down to maybe things like $\lambda \approx 0.001 \: Å$, but the further down you get, the less applicable that language becomes (so, say, something like $\lambda \approx 10^{-20} \: Å$ would not be included in that usage, as it's just too small). Since the construction is fuzzy, though, there is no hard bottom at which the length is too small to qualify.

And as for the fraction $1\: Å/1 \: Å$, that is a dimensionless number and not a length, so a wavelength cannot be equal to that.

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It's saying that the de Broglie wavelength of an electron can be less than an angstrom

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