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I am a theoretical physics student and am a little ashamed at my inability to estimate any measurable quantity. I would like to develop my skills at Fermi estimations.

Although it is hopeless to start memorising physical constants, I would like to ask if there there is a compact list of quantities that are easy to memorise and useful in varied contexts to know?

For example, I learned today that a mole of Boltzmann constants is $k_B \, 10^{23} \cong 8.3$ in SI units and that, at room temperature, $k_B T \cong 1/40$ $eV$.

If someone knows where I can find a list of such tricks I would very much like to know about it.

Also, If you know one or two of these tricks, I will be happy to learn about them and make the list myself.

David Bailey
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Steven Mathey
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1 Answers1

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If you consider it hopeless to memorize physical constants, it will probably help to find combinations of these constant that relate to the human scale. For instance:

  • The gravitational constant $G$ might be difficult to memorize. This holds for both the units as well as the value. However, multiply this constant by the density of water, take the square root, and you end up with a characteristic frequency of about one per hour: $\sqrt{G \rho_w} \approx$ one per hour. If you memorize this fact, and provided you know the density of water in your preferred system of units, you can always work back to the value of $G$.

  • The quantum of action $\hbar$ and the elementary charge $e$ lead to tiny values when evaluated in any day-to-day system of units. However, the ratio $\hbar / e^2 \approx 4 k \Omega$, a value more easy to remember.

  • A similar relation holds for $\hbar $ and the electron mass $m_e$ their ratio gives a diffusion constant: $\hbar/m_e \approx$ one square centimeter per second.

You can augment the above with other ratios of fundamental constants that are easy to remember, such as $\sqrt{\hbar c/G} \approx 22 \mu g$ (the Planck mass), as well as with the values of dimensionless constants such as the fine structure constant.

Johannes
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