When beryllium-7 ions (m=11.65E-27 kg) pass through a massspectrometer, a unifor

Question

When beryllium-7 ions (m=11.65E-27 kg) pass through a massspectrometer, a uniform magnetic field of 0.283T curves their pathdirectly to the center of the detector. For the same acceleratingpotential difference, what magnetic field shuld be used to sendberyllium-10 ions (m=16.63E-27 kg) to the same location in thedetector? Both types of ions are singly ionized (q=+e). Please Help! When beryllium-7 ions (m=11.65E-27 kg) pass through a massspectrometer, a uniform magnetic field of 0.283T curves their pathdirectly to the center of the detector. For the same acceleratingpotential difference, what magnetic field shuld be used to sendberyllium-10 ions (m=16.63E-27 kg) to the same location in thedetector? Both types of ions are singly ionized (q=+e). Please Help!

Explanation / Answer

the idea is that the acc potential diff gives the ions theirspeed .      elec potential energy = KE of ions .            qV = (1/2) mv2      . Then the B field bends them in a circle .        centrip force = magnetic force .            mv2 / r =   q v B .           2 q V /r   = q (2 q V / m )1/2 B .           2V   =   (2 q V / m )1/2 Br . Notice that in your problem,   V and q are the same for both ions. Only m and B are different. . We can write, for the first ion: .           2V m   = 2qV   Br          . And the same thing for the second ion. . Then divide the two expressions and you get just a ratio ofmasses and B fields (because everything else divides out) .       ( m2 /m1 )   = B2 /B1            solve for B2 .     B2   = B1 ( m2 / m1)1/2 = 0.283 * (16.63 /11.65)1/2   =    0.338 T    is the mag field you need for the secondion

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

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