Mass Spectrometer: Separating Ions & Calculating Energy

[llabesabusp]

If I was given that a mass spectrometer was used to separate ions of mass 3.92x10^-25 kg and charge 3.20x10^-19 C from other ions and the ions were accelerated through a potential difference of 80 kV and then sent into a uniform magnetic field, where they were bent in a path of radius 0.60 m and after traveling 180° passed through a slit of width 1.00 mm and height 1.00 cm, where they were collected into a cup:

Also, the magnetic field, B, is 0.737865 T.

(a) How would I find the current if the machine was to separate out 80 mg of material per hour?
(b) How would I calculate the thermal energy produced in the cup in 1 hour?

 

[Redbelly98]

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[nlightner]

(a) To find the current, we can use the formula I = Q/t, where I is the current, Q is the charge, and t is the time. In this case, we know that the charge of the ions is 3.20x10^-19 C and the time is 1 hour or 3600 seconds. Therefore, the current would be:

I = (3.20x10^-19 C)/(3600 s) = 8.89x10^-23 A

(b) To calculate the thermal energy produced in the cup in 1 hour, we can use the formula E = P*t, where E is the energy, P is the power, and t is the time. In this case, we need to first calculate the power, which is given by the formula P = IV, where I is the current and V is the potential difference. So, the power would be:

P = (8.89x10^-23 A)(80 kV) = 7.11x10^-20 W

Now, we can calculate the energy by multiplying the power by the time:

E = (7.11x10^-20 W)(3600 s) = 2.56x10^-16 J

This is the thermal energy produced in the cup in 1 hour.