A proton, deuteron, and an alpha particle in a region with a uniform magnetic fi

Question

A proton, deuteron, and an alpha particle in a region with a uniform magnetic field each follow circular paths that have the same radius. The deuteron has a charge that is equal to the charge a proton has, and an alpha particle has a charge that is equal to twice the charge a proton has. Assume that m = 2md = 4mp.
(a) Compare their speeds.
vp =______ · vd = ______ · v

(b) Compare their kinetic energies.
Kp =______· Kd =________· K

(c) Compare the magnitudes of their angular momenta about the centers of the orbits.
Lp =______· Ld = _______· L

Explanation / Answer

radius r = mv/qB where m is mass, v is velocity, q is charge, B is magnetic field

a)

v = qBr/m

Vp = qp*B*r/mp = k

Vd = qd*B*r/md = qp*B*r/2mp = k/2

V = q*B*r/m = 2qp*B*r/(4mp) = k/2

so if proton has a speed k then deuteron and has k/2

b)

kinetic energy of proton = 1/2*mp*vp^2 = 1/2*mp*k^2 = K.E

kinetic energy of deutern = 1/2*md*vd^2 = 1/2*2mp*(k/2)^2 = 1/2*K.E

kinetic energy of alpha = 1/2*m*v^2 = 1/2*4mp*(k/2)^2 = K.E

so proton and alpha has same inetic energy while deuteron has half of that

c)

angular momentum of proton = mp*vp*r = mp*k*r = L

angular momentum of deuteron = md*vd*r = 2mp*k/2*r = L

angular momentum of alpha = m*v*r = 4mp*k/2*r = 2L

proton and duteron has same angular momentum while alpha particle has twice of that

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.