Can You Fit the Entire Encyclopaedia Britannica on a Pinhead?

[CampRock]

Homework Statement

Richard Feynman propsed writing the entrie Encyclopaedia Brittanica on the head of a pin.
1) Estimate the size of the letters needed if we suppose a pinhead is 1/16 in across.
2) If the atomic spacing is 5x10^(-10)m, how many atoms across is each letter?

Homework Equations

The Attempt at a Solution

So I assume that the average Britannica contains 50 million words, but what I need is the average areas of a pinhead compared to Britannica (which I can't figure out how to get values of).
I've also estimated the answer to be 10^(-8) atoms from some articles I have read, but I unfortunately can't come up how to get that solution.

A little help please? It's due tomorrow morning

 

[Hootenanny]

Welcome to Physics Forums.

You are given the size of the pinhead, assuming that it is circular, you can then determine the area of the pin head.

The next step is then to estimate the average number of letters in a word - such things are undoubtedly available on the internet.

 

[Architeuthis Dux]

!

I would start by acknowledging that Feynman's proposal is a thought experiment and not a practical or feasible idea. The concept is meant to highlight the vast amount of information that can be contained in a small space.

For the first question, to estimate the size of the letters needed, we can make some assumptions. Let's assume that each word in Britannica contains an average of 6 letters and there are 50 million words, that would mean there are approximately 300 million letters in the encyclopedia. If we divide that by the area of a pinhead (1/16 in²), we get an average of 18.75 million letters per square inch. This means that each letter would need to be extremely small, around 0.0000000533 inches in size.

For the second question, we can use the formula A = L^2, where A is the area and L is the length of each side of the letter. Since we know the area of a pinhead (1/16 in²) and the atomic spacing (5x10^-10 m), we can set up the following equation:

1/16 in² = (L x 5x10^-10 m)^2

Solving for L, we get L = 1.12x10^-9 m. This means that each letter would be approximately 1.12 nanometers in size.

To determine how many atoms across each letter would be, we can divide the length of the letter (1.12x10^-9 m) by the atomic spacing (5x10^-10 m). This gives us approximately 2.24 atoms across each letter.

It's important to note that these calculations are based on assumptions and estimations, and the actual size and number of atoms across each letter may vary. However, it gives us a general idea of the scale and magnitude of Feynman's thought experiment.