A deuteron is a charged particle that has the same charge as a proton but approx
ID: 1447697 • Letter: A
Question
A deuteron is a charged particle that has the same charge as a proton but approximately twice the mass. An alpha particle has twice the charge and approximately four times the mass of a proton. For this problem, assume the mass ratios are exactly 2 and 4. A proton, a deuteron, and an alpha particle move in a uniform magnetic field in circles having the same radii. Compare the speeds of a deutron and a proton. Compare the speeds of an alpha particle and a proton. Compare the kinetic energies of a deutron and a proton. Compare the kinetic energies of an alpha particle and a proton. Compare the angular momentum magnitudes of a deutron and a proton. Compare the angular momentum magnitudes of an alpha particle and a proton.
Explanation / Answer
Given that :
charge on deutron particle, qd = +1.6 x 10-19 C
mass of deutron particle, md = 2 (1.67 x 10-27 kg)
charge on alpha partilce, qa = 2 (1.6 x 10-19 C)
mass of alpha partilce, ma = 4 (1.67 x 10-27 kg)
A proton, a deuteron, and an alpha particle move in a uniform magnetic field in circles having the same radii.
using a formula, we have
r = m v / q B
(a) To compare the speeds of a deutron and a proton which is given as :
vd / vp = (qd B r / md) / (qp B r / mp)
vd / vp = [(1.6 x 10-19 C) / (3.34 x 10-27 kg)] / [(1.6 x 10-19 C) / (1.67 x 10-27 kg)]
vd / vp = 0.5
(b) To compare the speeds of an alpha particle and a proton which is given as :
va / vp = (qa B r / ma) / (qp B r / mp)
va / vp = [(3.2 x 10-19 C) / (6.68 x 10-27 kg)] / [(1.6 x 10-19 C) / (1.67 x 10-27 kg)]
va / vp = 0.5
(c) To compare the kinetic energies of a deutron and a proton which is given as :
K.Ed / K.Ep = (1/2) md vd2 / (1/2) mp vp2
K.Ed / K.Ep = [2 (1.67 x 10-27 kg) / (1.67 x 10-27 kg)] (0.5)2
K.Ed / K.Ep = 0.5
(d) To compare the kinetic energies of a alpha particle and a proton which is given as :
K.Ea / K.Ep = (1/2) ma va2 / (1/2) mp vp2
K.Ea / K.Ep = [4 (1.67 x 10-27 kg) / (1.67 x 10-27 kg)] (0.5)2
K.Ea / K.Ep = 1
(e) To compare the angular momentum magnitudes of a deutron and a proton which is given as :
Ld / Lp = md vd r / mp vp r
Ld / Lp = md vd / mp vp = [(2 (1.67 x 10-27 kg) / (1.67 x 10-27 kg)] [(0.5)]
Ld / Lp = 1
(e) To compare the angular momentum magnitudes of a deutron and a proton which is given as :
La / Lp = ma va r / mp vp r
La / Lp = ma va / ma vp = [(4 (1.67 x 10-27 kg) / (1.67 x 10-27 kg)] [(0.5)]
La / Lp = 2
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