A relatively new method of treating cancers is to bombard the tumor with protons

Question

A relatively new method of treating cancers is to bombard the tumor with protons (The nuclei of hydrogen). The idea is that the protons will eject electrons from the molecules of the cell, and then electrostatic forces (discussed in physics 1202W) will then pull the molecule apart. If this happens in the cell DNA, the cell will be sterile and thus will not reproduce but will disappear after its natural lifetime.

Electrons are however bound to their individual atoms, which mean that relative to the world they have negative potential energy. It is therefore necessary to transfer energy to them in order to release them.

Consider the most favorable case. A proton collides head on with an electron, so that after the collision, they both leave in the same direction as the proton was incident.. The collision is elastic, i.e. no loss of energy, and the average binding (potential) energy of the electrons in the tumor cells is -5 electron volts.

What is the minimum energy of the incoming proton which will eject an average electron? If instead of it being an elastic collision, the electron sticks to the proton to form a hydrogen atom, what then would be the minimum energy of the incoming proton?

( 1 electron volt = 6 x 10-18 Joules.

Mass of a proton 1..6 x 10- 27 Kg,

Mass of an electron 9.1 x 10-31 Kg).

Explanation / Answer

(1) In the first case the collision is elastic collision so according to conservation of energy. Energy of proton+Energy of electron = Binding energy Ep+0 = 5 eV (Initially the electron at rest) Ep = 5*6*10^-18 J = 30*10^-18 J velocity of the proton 30*10^-18 = 1/2*(1.6*10^_27kg()v^2) v^2 = 37.5*10^9 vp = 6.1*10^3 m/s _____________________________________________________________________________ (2) In second case the collision is inelastic so here only momentum is conserved mpup+meue =mpvp+meve momentum of the electron is zero becuause electron is in rest position by our consideraion mpup = (mp+me)v v = mpup/(mp+me) = (1.6*10^_27)( 6.1*10^3)/*(1.6*10^_27)(9.1 x 10-31) = 6.7*10^32 m/s k.E = 1/2mv^2 = 1/2(1.6*10^_27)( 6.7*10^32 m/s)^2

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