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2.48: How Many Bibles Can Fit on the Head of a Pin

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    On December 29, 1959 Richard Feynman gave an address (Thereʹs Plenty of Room at the Bottom) in which he calculated how many Encyclopedia Britannicas could fit on the head of a pin. Legend identifies this event as the beginning of the field of theoretical nanotechnology.

    To illustrate to general chemistry students how small nanoscopic entities, such as atoms, are I calculate with the following simple model how many bibles can fit on the head of a pin.

    The model assumes that the pinhead surface is made up of Fe atoms packed in a simple squaric array. It further assumes that letters would be made by placing adatoms in the pockets created by the surface Fe atoms using a scanning tunneling microscope, and that 100 pinhead surface Fe atoms would be required to form a letter.

    The first step is to calculate the number of Fe atoms on the pinhead.

    \[ \begin{matrix} \text{Radium of pinhead:} & R_{PH} = \frac{1}{32} in & R_{PH} = 7.94 \times 10^8 pm \\ \text{Area of pinhead:} & \text{Area}_{PH} = \pi R_{PH}^2 & \text{Area}_{PH} = 1.98 \times 10^{18} \text{pm}^3 \\ \text{Radius of Fe:} & \text{R}_{Fe} = 126 \text{pm} & \text{R}_{Fe} = 1.26 \times 10^{-10} \text{pm} \\ \text{Area of Fe atom:} & \text{Area}_{Fe} = \pi \text{R}_{Fe}^2 & \text{Area}_{Fe} = 4.99 \times 10^4 \text{pm}^2 \end{matrix} \nonumber \]

    Effective area of Fe atom:

    Screen Shot 2019-06-18 at 8.44.49 PM.png

    \[ \begin{matrix} \text{EffectiveArea}_{Fe} = 4 \text{R}_{Fe}^2 \\ \text{EffectiveArea}_{Fe} = 6.35 \times 10^4 \text{pm}^2 \end{matrix} \nonumber \]

    Fe atoms per pinhead:

    \[ \begin{matrix} \text{FeAtomsPerPinHead} = \frac{ \text{Area}_{PH}}{ \text{EffectiveArea}_{Fe}} & \text{FeAtomsPerPinHead} = 3.12 \times 10^{13} \end{matrix} \nonumber \]

    A typical family Bible consists of 1,000 pages with an average of 5,000 characters and spaces per page. If it takes 100 Fe atoms to define a character, how many Bibles can fit on the head of a pin?

    \[ \begin{matrix} \text{PagesPerBible} = 1000 & \text{CharactersPerPage} = 5000 & \text{FeAtomsPerCharacter} = 100 \end{matrix} \nonumber \]

    Fe atoms required per bible:

    \[ \begin{matrix} \text{FeAtomsPerCharacter CharactersPerPage PagesPerBible} = 5 \times 10^8 \\ \text{BiblesPerPinHead} = \frac{ \text{FeAtomsPerPinHead}}{ \text{FeAtomsPerCharacter CharactersPerPage PagesPerBible}} \\ \text{BiblesPerPinHead} = 6.2 \times 10^4 \end{matrix} \nonumber \]

    Define picometer: \( \text{pm} = 10^{-12} \text{m}\)

    This page titled 2.48: How Many Bibles Can Fit on the Head of a Pin is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Frank Rioux via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.