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Appendix B Problems

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Basic

Medium

Basic

B-1. SI Calculation of the Electron Compton Wavelength

Calculate the Compton wavelength of the electron \(\lambda_C = \hbar/(m_e c)\) in SI units.

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B-2. Planck Mass in GeV

Express the Planck mass \(m_P\) in GeV. How many times larger is it than the proton mass (\(\approx 0.938\) GeV)?

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Medium

M-1. Dimension of \(G\) in Natural Units

Confirm that the dimension of \(G\) in natural units is \([\text{E}]^{-2}\) (same as Problem 12.2 in Chapter 12).

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M-2. Fine-Structure Constant in Natural Units

Verify that in natural units, \(\alpha = e^2/(4\pi)\) (where \(\varepsilon_0 = 1\), \(\hbar = c = 1\)).

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