How Do Charge and Mass Affect Ion Acceleration in an Electric Field?

In summary, the question is asking about the detection times of 3H+ and 3He+ accelerated towards a detector in a constant E field. The answer is that both particles would have the same flight time, despite having different charges, because their net charges are both +1. This is because 3H+ has one proton and no electrons, while 3He+ has two protons, one neutron, and one electron.
  • #1
mpswee2
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Homework Statement



Assuming equal masses, how would the detection times of 3H+ and 3He+ compare [as they're both accelerated toward a detector in the direction of a constant E field]?

A) 3H+ would have a longer flight time than 3He+.

B) 3H+ would have a shorter flight time than 3He+.

C) 3H+ would have the same flight time as 3He+.

D) The radioactive 3H+ would always decay before detection.

Homework Equations



Now, I initially thought it was C: both would have the same flight time since they have equal masses and, therefore, equal velocities once PE (PE=QV) is completely converted to kinetic energy (v= sqrt(2KE/m)).

But I realized-- in an 'aha!' moment-- that, although they have equal masses, they have UNequal charge, Q. The helium ion has 2 protons and 1 e-, while the H+ ion has 1 proton and no e-. If the Q of He+ and H+ are not equal, their initial PE = QV will not be equal, so their KE will not be equal. Because He+ has a higher Q due to 2 protons, the He+ has higher initial PE and greater KE after acceleration. It's flight time to reach detector should be less (ie faster travel) than H+, which has less KE.

But C was the correct answer. Could someone point out where my reasoning is flawed? Apparently He+ and H+ have equal Q-values. Is this because they're both +1 cations? Does the ionic charge alone always tell us a particle's charge? As I understood, simply losing 1 e- (to form +1 cation) won't always equalize the charges between ions due to differential number of protons. The additional protons in He+ should account for a different (greater) overall Q compared to in H+-- no??

I guess, in the end, I'm curious how you determine an ions Q. Is Q always going to equal the overall ionic charge-- or do we need to take the number of protons into account when we have ions with equal charges?

Thanks a lot.

The Attempt at a Solution

 
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  • #2
3H+ has two neutrons, one proton and no electrons. 3He+ has two protons, one neutron and one electron. The net charge of both is the same, +1. The masses are almost (but not exactly) equal - but you are told to assume they are. Hence, C. The '+' symbol is indicating total charge.
 
  • #3


I would like to clarify that in this scenario, the detection times of 3H+ and 3He+ would be the same. This is because the acceleration of particles in an electric field is not dependent on their charge, but rather on their mass.

The equation for acceleration in an electric field is a = QV/m, where a is the acceleration, Q is the charge, V is the voltage, and m is the mass. In this case, we are assuming that the voltage and electric field are constant. Therefore, the acceleration of both particles would be the same, since they have the same mass.

Additionally, the initial potential energy (PE) of the particles, which is determined by their charge and voltage, will also be the same. This means that both particles will have the same initial kinetic energy (KE) after being accelerated. Since they have the same initial KE, their velocities will also be the same. This results in both particles reaching the detector at the same time, regardless of their charge.

In conclusion, the detection times of 3H+ and 3He+ would be the same in this scenario. It is important to remember that the acceleration of particles in an electric field is determined by their mass, not their charge.
 

FAQ: How Do Charge and Mass Affect Ion Acceleration in an Electric Field?

What is the purpose of accelerating ions in an E-field?

The purpose of accelerating ions in an E-field is to increase their kinetic energy, allowing them to move at higher speeds. This is useful in various fields of science, such as nuclear physics and medical research, where accelerated ions can be used for experiments and treatments.

How does an E-field accelerate ions?

An E-field, or electric field, is created by placing a positive charge at one end and a negative charge at the other end. Ions, which are charged particles, will be attracted to the opposite charge and repelled by the same charge. This attraction and repulsion causes the ions to accelerate in the direction of the electric field.

What factors affect the acceleration of ions in an E-field?

The acceleration of ions in an E-field is affected by the strength of the electric field, the charge of the ions, and the mass of the ions. A stronger electric field will result in a greater acceleration, while larger charges and lighter masses will also lead to higher accelerations.

What are some applications of accelerated ions in science?

Accelerated ions have many applications in science, including particle accelerators used in nuclear physics research, ion implantation for semiconductor manufacturing, and proton therapy for cancer treatment. They are also used in mass spectrometry, surface analysis, and materials characterization.

Are there any potential risks associated with accelerating ions in an E-field?

There are potential risks associated with accelerating ions in an E-field, such as radiation exposure, electrical hazards, and equipment malfunctions. Proper safety precautions and protocols should be followed when working with high-energy ions to minimize these risks.

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