Determine the velocity of a particle in mass spectrometry

AI Thread Summary
To determine the velocity of a particle in mass spectrometry, the relationship between potential energy (Ep) and kinetic energy (Ec) must be correctly applied. The equation Ep = 0.5 (sigma(i) qiVi) is valid for multiple charges, while for a single particle in an external field, Ep simplifies to U = qV. This distinction is crucial to avoid misapplication of the formulas. Clarification is needed on the origin of the equation Ec(f) = Ec(i) - Ec(f), as it appears to be incorrectly stated. Understanding the context and correct application of these equations is essential for accurate calculations.
duchuy
Messages
79
Reaction score
3
Homework Statement
V=3000V, B= 0,035 T, m = m = 2.10^(-26) kg, q = e
Relevant Equations
x
Hi, I am trying to determine the velocity of the particle with the mass m coming out of the acclerator.
I tried writing :
Ep(i) + Ec(i) = Ep(f) + Ec(f)
Ec(f) = Ec(i) - Ec(f)
But at this step, I'm no longer sure how to express Ep with V because :
In my textbook, it's written :
Ep = 0,5 (sigma(i) qiVi)
But I am not sure if I am supposed to put that 0,5 in this case or not, which would imply Ep = qV only.

Ep = potential energy
Ec = Kinetic energy
Sorry in advance if these aren't notations that are used in English.

Thank you so much for your help!
 
Physics news on Phys.org
duchuy said:
Homework Statement:: V=3000V, B= 0,035 T, m = m = 2.10^(-26) kg, q = e
Relevant Equations:: x

Ep = 0,5 (sigma(i) qiVi)
This is true for a collection of charges where the potentials are due to the same charges you are considering. This is to avoid double counting because in actuality the potentials are between pairs of charges. The text you are reading should explain this.

If you are considering a single particle in an external field, then potential energy is U = qV. This is an example of the need to understand formulae that you find and to make sure they are applicable.
 
Oh okay thank you sir!
 
A diagram would help in understanding what the symbols and the formulae mean.
I am not sure where the second formula
Ec(f) = Ec(i) - Ec(f), comes from.
 
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Thread 'Variable mass system : water sprayed into a moving container'
Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
Back
Top