Question

Sorry i was not given a charge in the problem, this is all the information i have! A mass spectrometer is being used to separate common oxygen-16 from the much rarer oxygen-18, taken from a sample of old glacial ice. (The relative abundance of these oxygen isotopes is related to climatic temperature at the time the ice was deposited.) The ratio of the masses of these two ions is 16 to 18, the mass of oxygen-16 is 2.66 × 10-26 kg, and they are both singly charged and travel at 4.85 × 106 m/s in a 1.25 T magnetic field.

What is the separation between their paths in meters when they hit a target after traversing a semicircle? Δd = |

Answer 1

As we know that the separation in the paths is measured after traversing a semicircle, the separation is the difference in diameter (2r).

$r=\frac{mv}{qB}$

$\Delta d=\frac{2(m_{18}-m_{16})v}{qB}$

$m_{18}-m_{16}=\frac{18-16}{18}\times 2.66\times 10^{-26}kg=3.33\times 10^{-27}kg$

$\Delta d=\frac{2(3.33\times 10^{-27}kg)(4.85\times 10^6)m/s}{(1.6\times 10^{-19}C)(1.25T)}$

$\Delta d=\frac{(3.23\times 10^{-20})}{(2\times 10^{-19})}$

$\Delta d=0.1615m$