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title: "A cyclotron with a uniform magnetic field \\(B\\) and maximum dee radius \\(R\\) is initially calibrated to accelerate protons of charge \\(+e\\) and mass \\(m\\). The cyclotron is then used to accelerate alpha particles, which have charge \\(+2e\\) and mass \\(4m\\). How do the required alternating electric field frequency \\(f_\\alpha\\) and the maximum achievable kinetic energy \\(K_{\\alpha,\\text{max}}\\) for the alpha particles compare to the corresponding quantities \\(f_p\\) and \\(K_{p,\\text{max}}\\) for the protons?"
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url: "https://nerd-notes.com/ubq/118488/"
date_modified: "2026-08-04T08:11:03+00:00"
---

# A cyclotron with a uniform magnetic field \(B\) and maximum dee radius \(R\) is initially calibrated to accelerate protons of charge \(+e\) and mass \(m\). The cyclotron is then used to accelerate alpha particles, which have charge \(+2e\) and mass \(4m\). How do the required alternating electric field frequency \(f_\alpha\) and the maximum achievable kinetic energy \(K_{\alpha,\text{max}}\) for the alpha particles compare to the corresponding quantities \(f_p\) and \(K_{p,\text{max}}\) for the protons?

A cyclotron with a uniform magnetic field \(B\) and maximum dee radius \(R\) is initially calibrated to accelerate protons of charge \(+e\) and mass \(m\). The cyclotron is then used to accelerate alpha particles, which have charge \(+2e\) and mass \(4m\). How do the required alternating electric field frequency \(f_\alpha\) and the maximum achievable kinetic energy \(K_{\alpha,\text{max}}\) for the alpha particles compare to the corresponding quantities \(f_p\) and \(K_{p,\text{max}}\) for the protons?

- **A.** \(f_\alpha = \dfrac{1}{2} f_p\) and \(K_{\alpha,\text{max}} = \dfrac{1}{2} K_{p,\text{max}}\)
- **B.** \(f_\alpha = \dfrac{1}{2} f_p\) and \(K_{\alpha,\text{max}} = K_{p,\text{max}}\)
- **C.** \(f_\alpha = f_p\) and \(K_{\alpha,\text{max}} = 2 K_{p,\text{max}}\)
- **D.** \(f_\alpha = 2 f_p\) and \(K_{\alpha,\text{max}} = K_{p,\text{max}}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/118488/*