Problem P. 4222. (January 2010)

P. 4222. Three times ionized UF₆ molecules are accelerated through a voltage of 5 kV, and then through a small hole they are led to a region of magnetic field of induction 1 T. The induction vector is perpendicular to the velocity of the molecules.

a) What is the path of the ions? Give the characteristic parameters of the paths of the ions which contain the 238 and the 235 isotopes of the Uranium.

b) In this way the two Uranium isotopes can be separated. During the Second World War the available ion sources could produce an ion current of 1 mA. How long would it have taken to separate 1 kg pure ²³⁵U isotope with this method?

(4 pont)

Deadline expired on February 10, 2010.

Sorry, the solution is available only in Hungarian. Google translation

Megoldás. \(\displaystyle a)\) A pálya \(\displaystyle R=\sqrt{\frac{2Um}{3eB^2}}\) sugarú kör, \(\displaystyle R_{238}=11,07\) cm, \(\displaystyle R_{235}=11,02\) cm.

\(\displaystyle b)\) A természetes urán 0,7%-a 235-ös izotóp, így kb. 5500 évre lett volna szükség.

Statistics:

42 students sent a solution.
4 points:	Balogh Gábor, Batki Bálint, Benyó Krisztián, Béres Bertold, Bolgár Dániel, Csopor Dávid, Farkas Martin, Janosov Milán, Jéhn Zoltán, Kovács Márk, Kungl Ákos Ferenc, Lájer Márton, Molnár Alexandra, Nagy 111 Miklós, Patartics Bálint, Pázmán Koppány, Szabó 928 Attila, Varju 105 Tamás, Várnai Péter, Vuchetich Bálint.
3 points:	Filep Gábor, Fonai Dániel, Hoksza Zsolt, Kovács 616 Philip, Laczkó Zoltán Balázs, Pál Domonkos, Pető János, Réti Dávid, Sápi András, Vécsey Máté.
2 points:	10 students.
Unfair, not evaluated:	2 solutionss.

Problems in Physics of KöMaL, January 2010