Calculating Magnetic Field & Thermal Energy in a Mass Spectrometer

[claire1]

A mass spectrometer is used to separate uranium ions of mass 3.92e-25 kg and charge 3.2e-19 C from related species. The ions are accelerated through a potential difference of 100 kV and then pass into a uniform magnetic field, where they are bent in a path of radius 1.00 m. After traveling through 180 degrees and passing through a slit of width 1.00 mm and height 1.00 cm, they are collected in a cup. a) What is the magnitude of the (perpendicular) magnetic field in the separator? If the machine is used to separate out 100 mg of material per hour, calculate b) the current of the desired ions in the machine and c) the thermal energy produced in the cup in 1.00 h.

I understand how to solve part a and part b, but I am confused about how to find the thermal energy produced in the cup (part c). I know that I will have to somehow convert to joules for thermal energy, but I can't figure out where to start.

 

[dstorm]

You just focus on your units and do dimensional analysis. Start 100 mg/hr, then convert to kilograms, multiply by an hour, multiply by the 3.2e19c/3.92e-25kg, and then finish up with multiplying by 1e5J/1c and your final answer should be in Joules! Cancel your units and double check.

 

[I like Serena]

A mass spectrometer is used to separate uranium ions of mass 3.92e-25 kg and charge 3.2e-19 C from related species. The ions are accelerated through a potential difference of 100 kV and then pass into a uniform magnetic field, where they are bent in a path of radius 1.00 m. After traveling through 180 degrees and passing through a slit of width 1.00 mm and height 1.00 cm, they are collected in a cup. a) What is the magnitude of the (perpendicular) magnetic field in the separator? If the machine is used to separate out 100 mg of material per hour, calculate b) the current of the desired ions in the machine and c) the thermal energy produced in the cup in 1.00 h.

I understand how to solve part a and part b, but I am confused about how to find the thermal energy produced in the cup (part c). I know that I will have to somehow convert to joules for thermal energy, but I can't figure out where to start.

Hi claire! Welcome to MHB! :)

I take it you have calculated the speed of the ions in part (a)?

That means you can also calculate the kinetic energy of 100 mg worth of ions.
This kinetic energy is converted to thermal energy without loss.

Alternatively, you can calculate the electric energy transferred by 100 kV voltage difference to 100 mg worth of ions. This energy will ultimately be converted to thermal energy.