A sample containing elements with atomic masses m 1 =30 and m 2 =13 and an unkno

Question

A sample containing elements with atomic masses m1=30 and m2=13 and an unknown element is placed into a mass spectrometer. The ions all have the same charge and are accelerated to the same initial velocity before they enter the magnetic field. On the surface of the detector of the spectrometer the lines corresponding to elements with m1and m2  are separated by separation1=3.3 cm. The unknown element is detected to the right of element with m2, separation2=8.0 cm from it.

What is the mass of the unknown element? The answer should be in "amu" units.

Explanation / Answer

Here , let the unknown mass is m3

Now , as the radius of the path is given a

r = m*v/(B*q)

as the ions have same charge and same magnetic field , initial velocity

seperation between m1 and m2 =

r1- r2 = 2 * (m1 - m2) *v/(B*q)

3.3 = 2 *(30 - 13) * v/(B*q)

v/(B*q) = 3.3/(34)

Now , for seperation between m3 and m2

r3 - r2 = 2 *(m3 - m2) * v/(B*q)

8 = 2 *(m3 - 13) * 3.3/34

m3 = 54.2 amu

the unknown element is 54.2 amu

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