A Helium Nucleus (also known as an alpha particle) is placed on the positive pla

Question

A Helium Nucleus (also known as an alpha particle) is placed on the positive plate of a parallel plate capacitor as shown in the drawing. It is initially at rest. The Helium Nucleus then moves toward the negative plate. The potential difference across the capacitor is 200 volts. The distance between the plates is d = 0.013 m. {Ignore gravitational effects in this problem.} What speed does the Helium Nucleus have when it reaches the negative plate? What is the magnitude of the electric field across the plate (before the Helium Nucleus is introduced)? Nucleus has 2 protons and 2 neutrons. Only the 2 protons have an electric charge. also need to obtain a mass (in kg) for the helium nucleus.

Explanation / Answer

mass of he = 2*mass of proton + 2* mass of neutron , m= 2*1.67*10^-27 +2*1.67*10^-27 = 6.4 * 10^-27 kg.

charge on nucleaus ,Q = 2* charge on proton= 2* 1.6 * 10^-19 C

Force on nucleaus = electric field * charge

electric field = V/d

so force= V/d*Q

force = ma

so a = V*Q/(d*m)

if v is final veloctit and u is initial then v^2- u^2=2*a*s since u =0

v= (2*a*s)^1/2 = (2*V*Q/(d*m)*d)^1/2 = (2*200*3.2*10^-19/6.4*10^-27)^1/2 = 1.42*10^5 m/s

Electric field = V/d = 200//.013 = 15384.615 V/m

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