Question

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 5.15 × 106 m/s in a 1.25 T magnetic field.

Answer 1

Answer:

The separation between their paths is 7.6 cm.

Explanation:

Suppose we find the separation between their paths when they hit a target after traversing a semicircle?

Given that,

Mass of oxygen-16 $m_{o}= 2.66\times10^{-26}\ kg$

The ratio of the masses of these two ions is 16 to 18,

Speed $v= 5.15\times10^{6}\ m/s$

Magnetic field B = 1.25 T

We need to calculate the radius

Using formula of radius

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

The radius of oxygen-16

$r_{1}=\dfrac{m_{1}v}{qB}$

The radius of oxygen-18

$r_{2}=\dfrac{m_{2}v}{qB}$

We need to calculate the separation between their paths

The separation between their paths

$\Delta r=r_{2}-r_{1}$

$\Delta r=\dfrac{m_{2}v}{qB}-\dfrac{m_{1}v}{qB}$

Put the value into the formula

$\Delta r=\dfrac{5.15\times10^{6}}{1.6\times10^{-19}\times1.25}(2.66\times10^{-26}-\dfrac{16}{18}\times2.66\times10^{-26})$

$\Delta r=7.6\times10^{-2}\ m$

$\Delta r=7.6\ cm$

Hence, The separation between their paths is 7.6 cm.