Chapter 20, Problem 23Q

To determine

How the positions of ion on the film of mass spectrometer differ?

Answer to Problem 23Q

Solution:

Ions are separated by $2:1$ on the mass spectrometer.

Explanation of Solution

Given:

Mass of both the ion is same, $m_1=m_2=m$

Charge of both the ion, $Q_1=q$

Charge of the other ion, $Q_2=2q$

Formula used:

The ions inside the mass spectrometer travel in a circular path.:

Magnetic force= centripetal force:

$QvB=\frac{m{v}^2}{r}$

•Q is the charge of ions

•‘v’ is the velocity of ions

•B₂ is the magnetic field.

•‘r’ is the separation distance

•‘m’ is the mass of the ion

Calculation:

The mass of the ions is given as

$m_1=\frac{Q_{1}B{r}_1}{v}$

Since both the ions have equal mass therefore

$\begin{array}{c}{m}_1=m_2\\ \frac{Q_{1}B{r}_1}{v}=\frac{Q_{2}B{r}_2}{v}\\ \frac{r_1}{r_2}=\frac{Q_2}{Q_1}=\frac{2q}{q}=2:1\end{array}$