Question

in a mass spectrometer ionized molecules are accelerated from rest through a potential difference V into a uniform magnetic field. only those molecules with the correct mass will have the travel radius that allows them to go through the hole and into the detector. what potential differeence is needed so that singly ionized carbon dioxide molecules

Answer 1

Answer:

Potential difference = 245 V

Explanation:

First, we have to find velocity at which ionized molecules are accelerated into a magnetic field. Here, magnetic force acts as a centripetal force due to circular path of molecules towards detector slot.

• B= 0.25 T,d= 12 cm
• mass = (12+16+16)×1.67×10-27kg

Now, the magnetic force to the centripetal force equates as:

qvB = $\frac{mv2}{r}$ = $\frac{mv2}{d/2}$

For Velocity (v) :

v = $\frac{qBd}{2m}$

According to law of conservation of energy, we know that the initial potential energy of the molecules is converted into kinetic energy as they enter into the magnetic field. So,

$qV=\frac{1}{2}mv2$

Substitute the value of v in above equation:

qV = $\frac{1}{2}$ m $\frac{q2B2d2}{4m2}$

V = $\frac{qB2d2}{8m}$

V= 245 V