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6. An experiment is set up to demonstrate a simple particle accelerator - Scottish Highers Physics - Question 6 - 2018
Question 6
6. An experiment is set up to demonstrate a simple particle accelerator. (a) Electrons are accelerated from rest between the cathode and the anode by a potential di... show full transcript
Worked Solution & Example Answer:6. An experiment is set up to demonstrate a simple particle accelerator - Scottish Highers Physics - Question 6 - 2018
Step 1
Show that the work done in accelerating an electron from rest is 2.6 × 10^{-16} J.
Answer
The work done, W, in moving a charge, Q, through a potential difference, V, is given by the formula: Here, the charge of an electron is approximately C, and the potential difference is 1.6 kV, which is V.
Calculating the work done: Thus, the presented value is approximately J.
Step 2
Calculate the speed of the electron as it reaches the anode.
Answer
The kinetic energy (K.E.) gained by the electron when it is accelerated through the potential difference can be expressed as: K.E. = rac{1}{2} mv^2 where m is the mass of the electron ( kg) and v is its speed.
Equating the kinetic energy to the work done: rac{1}{2} mv^2 = W Substituting the values: So, 2.56 × 10^{-16} = rac{1}{2} (9.11 × 10^{-31}) v^2 Rearranging gives: v^2 = rac{2 × 2.56 × 10^{-16}}{9.11 × 10^{-31}} Calculating yields: Thus, taking the square root,
Step 3
Suggest one change that is observed.
Answer
As the potential difference increases, the screen will appear brighter. This is because the electrons will gain more energy and move faster, resulting in more intense collisions with the fluorescent material on the screen. The increased energy means either a brighter glow due to more electrons hitting the screen per second or an increase in brightness as the individual electrons possess more kinetic energy.
Step 4
Using your knowledge of physics comment on the model compared to a real particle accelerator, such as the large hadron collider at CERN.
Answer
The model of a particle accelerator that a student builds can demonstrate basic principles, such as acceleration and collision, but it lacks the sophistication and scale of a real particle accelerator like the LHC. In real accelerators, particles are accelerated to speeds close to the speed of light and can collide at extremely high energies, allowing for the investigation of fundamental particles. Furthermore, the LHC uses strong magnetic fields to maintain particle beams, which is not represented in a simple model. The mechanisms of control and measurement of particle behaviors in the LHC are highly advanced and involve extensive scientific instrumentation, unlike the simplified approach in classroom models.