Concept:In the high-energy radiation spectrum, wavelength is inversely proportional to photon energy and frequency according to the Planck-Einstein relation \(E = \frac{hc}{\lambda}\).
Formula / Reaction:$$\lambda = \frac{c}{f}$$
Solution:- Cosmic rays consist of ultra-high-energy astronomical particles and photons with frequencies exceeding \(10^{22}\text{ Hz}\) and wavelengths shorter than \(10^{-14}\text{ m}\).
- X-rays have wavelengths typically ranging between \(10^{-8}\text{ m}\) and \(10^{-11}\text{ m}\).
- Therefore, cosmic ray photons have the shortest wavelength among the choices.
Why other options are incorrect:- Opt_A: \(\alpha\)-rays are helium nuclei (matter particles), not electromagnetic waves.
- Opt_C: \(\beta\)-rays are fast electrons/positrons (matter particles), not electromagnetic waves.
- Opt_D: X-rays have longer wavelengths than cosmic ray photons.
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