A sample containing beryllium (atomic mass 9 u), aluminum (27 u), and an unknown

Question

A sample containing beryllium (atomic mass 9 u), aluminum (27 u), and an unknown element is placed in a mass spectrometer. The ions all have the same charge and are accelerated through the same potential difference before entering the magnetic field. The beryllium and aluminum lines are separated by 2.050 cm on the photographic plate, and the unknown element makes a line between them that is 0.565 cm from the beryllium line.
(a) What is the mass of the unknown element?




(b) Identify the element, using its chemical symbol. (Note that there may be more than one correct answer.)

Explanation / Answer

The Lorentz force provides the centripetal force: q v B = m v^2 / R, so m= qBR/v (1) As all the ions traverse the same potential difference, we know that their speed satisfies: q V = 1/2 m v^2 This means that v= sqrt(2qV/m) Substitution into (1) then gives m = qBR/sqrt(2qV/m) Isolating m gives m as a function of the radius R (q , B and V are constant): m = q B^2 R^2 / (4 V)= c R^2, where c is a constant for this experiment. With this you can find the relative masses.

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