Engineering problem (acceleration of ions)

In summary, the conversation discusses the use of parallel metal plates to separate fast moving ions from slow moving ones in a device designed to sample atmospheric pollution. A high voltage is applied to the plates, causing the ions to have a constant acceleration towards one plate and away from the other. The boss asks for the calculation of the necessary acceleration to separate ions with velocities of 100 m/s and 1000 m/s by 2.0 cm. Constant acceleration formulas and the time during which ions accelerate are also mentioned.
  • #1
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1. Acceleration between plates

You have a summer job as an assistant in a University research group that is designing a devise to sample atmospheric pollution. In this device, it is useful to separate fast moving ions from slow moving ones. To do this the ions are brought into the device in a narrow beam so that all of the ions are going in the same direction. The ion beam then passes between two parallel metal plates. Each plate is 5.0 cm long, 4.0 cm wide and the two plates are separated by 3.0 cm. A high voltage is applied to the plates causing the ions between them to have a constant acceleration directly toward one of the plates and away from the other plate. Before the ions enter the gap between the plates, they are no longer accelerated during the 50 cm journey to the ion detector. Your boss asks you to calculate the magnitude of acceleration between the plates necessary to separate ions with a velocity of 100 m/s from those in the beam going 1000 m/s by 2.0 cm?

2. constant acceleration formulas, parabolic path:

y= y0 + vy0 *t + 1/2(a)t^2
x= x0 + vx0 *t




3. Time during which ions accelerate (calculated with the equation: x=x0 + V0xt , for each ion):
t1=5*10^-5 t2=5*10^-4
 
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  • #2
Welcome to PF.

The 2 cm distance is at 50 cm.

What component of velocity is required to get the slow ion to deflect farther by 2 cm by the time it reaches 50 cm than the fast one?

You know V⊥ = a*t where t is the time the particle is subjected to acceleration between the plates.

That velocity times the time T to get to 50 cm at the original speed then would be the deflection I'd think for each particle. The additional constraint will be that 1 is 2 cm further along when it gets there. One distance will be deflected 2 cm more than the other.
 
  • #3


4. Acceleration between plates:

To calculate the acceleration between the plates, we can use the formula a= (Vf-Vi)/t, where Vf is the final velocity, Vi is the initial velocity, and t is the time during which the ions accelerate between the plates.

For the ions with a velocity of 100 m/s, the final velocity (Vf) is 0 m/s since they are stopped by the plates. The initial velocity (Vi) can be calculated using the formula x=x0 + V0xt, where x is the distance between the plates (2 cm), x0 is the initial distance (0 cm), and t is the time during which the ions accelerate (t1=5*10^-5). This gives us an initial velocity of 4000 m/s for the ions with a velocity of 100 m/s.

For the ions with a velocity of 1000 m/s, the final velocity (Vf) is also 0 m/s. The initial velocity (Vi) can be calculated in the same way, giving us an initial velocity of 40000 m/s.

Plugging these values into the acceleration formula, we get a= (0-4000)/5*10^-5 = -80,000,000 m/s^2 for the ions with a velocity of 100 m/s and a= (0-40000)/5*10^-4 = -800,000,000 m/s^2 for the ions with a velocity of 1000 m/s.

Therefore, the magnitude of acceleration between the plates necessary to separate these two ions is 800,000,000 m/s^2. This high acceleration will cause the slower ions to be deflected more than the faster ions, resulting in a separation between the two groups as they exit the plates.
 

Related to Engineering problem (acceleration of ions)

1. What is an engineering problem related to acceleration of ions?

An engineering problem related to acceleration of ions is the development of efficient and precise methods for accelerating ions in particle accelerators or ion propulsion systems.

2. How is the acceleration of ions used in scientific research?

The acceleration of ions is used in scientific research to study the properties of matter, such as the structure of atoms and molecules, and to create high-energy collisions for testing theories in particle physics.

3. What are some challenges in engineering ion acceleration systems?

Some challenges in engineering ion acceleration systems include designing powerful and stable electromagnetic fields, minimizing energy losses, and controlling the direction and speed of accelerated ions.

4. How does the acceleration of ions play a role in space travel?

In space travel, ion acceleration is used in ion thrusters to propel spacecrafts at high speeds with minimal fuel consumption. This technology is particularly useful for long-distance missions, such as interplanetary travel.

5. What are potential applications of ion acceleration technology?

Potential applications of ion acceleration technology include medical treatments, such as cancer therapy using ion beams, and industrial processes, such as ion implantation for enhancing material properties in manufacturing.

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