Consider an electron undergoing cyclotron motion in a magnetic field According to Bohr, the electrons angular momentum must be quantized in units of a Show that allowed radii for the electrons orbit are given by r n (n eB) 1 2 , where n 1, 2, 3, b Compute the first four allowed radii in a 1 0 T magnetic field c Find an expression for the allowed energy levels E n in terms of and the cyclotron frequency f cyc

Question: Consider an electron undergoing cyclotron motion in a magnetic field. According to Bohr, the electrons angular momentum must be quantized in units of . a.

Consider an electron undergoing cyclotron motion in a magnetic field. According to Bohr, the electron’s angular momentum must be quantized in units of ℏ.
a. Show that allowed radii for the electron’s orbit are given by r_n = (nℏ/eB)^1/2, where n = 1, 2, 3, ….
b. Compute the first four allowed radii in a 1.0 T magnetic field.
c. Find an expression for the allowed energy levels E_n in terms of ℏ and the cyclotron frequency f_cyc.

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