Question

Double ionize oxygen atoms (O2-) and singly-ionized lithium atoms (Li+) are traveling with the same speed, perpendicular to a magnetic field which causes them to move in circular orbits. The relative atomic masses of oxygen and lithium are 16 and 7 respectively. What is the ratio radius of )2- orbit/radius of Li+ orbit?

A. 16/7
B. 8/7
C. 7/8
D. 7/16
E. 7/32

Answer 1

A useful equation relating radius of orbit to mass and charge in a magnetic field is:
\[r=\frac{mv}{qB}\]From this, we know that:\[r\ \alpha\ \frac{m}{q}\]From this, we can compare the mass-to-charge ratios of each atom directly:
\[\frac{r_{O}}{r_{Li}}=\frac{\frac{m_{O}}{q_{O}}}{\frac{m_{Li}}{q_{Li}}}=\frac{\frac{16}{2}}{\frac{7}{1}}=\frac{8}{7}\]

Answer 2

thank you :)