Question

A Van de Graaff generator is one of the original particle accelerators and can be used to accelerate charged particles like protons or electrons. You may have seen it used to make human hair stand on end or produce large sparks. One application of the Van de Graaff generator is to create X-rays by bombarding a hard metal target with the beam. Consider a beam of protons at 1.00 keV and a current of 5.00 mA produced by the generator. (a) What is the speed of the protons? (b) How many protons are produced each second?

Answer 1

Answer:

a)    v = 4.38 10⁵ m / s,  b)      #_proton = 3.1 10¹⁶ protons

Explanation:

A) for this part we can use conservation of energy

starting point. Fight where the protons come out

          Em₀ = U = qV

final point. Fight where the protons arrive

          Em_f = K = ½ m v²

energy is conserved

           Em₀ = Em_f

           q V = ½ m v²

           v² = 2qV / m

let's calculate

           v² = $\frac{2 \ 1.6 \ 10^{-19} \ 1.00 \ 10^3}{ 1.67 \ 10^{-27}}$

           v = $\sqrt{19.16 \ 10^{10}}$

           v = 4.38 10⁵ m / s

B) For this part we can use a direct proportion rule or a res rule. If 1 proton creates a current of (q / t = 1.6 10-19 A), how many protons create a current of 5.00 10-3 A

            # _proton = 5 10⁻³ A ($\frac{1 proton }{1.6 \ 10^{-19} A}$)

            #_proton = 3.1 10¹⁶ protons