You want to reproduce Ernest Rutherford’s scattering experiments that led to the

Question

You want to reproduce Ernest Rutherford’s scattering experiments that led to the discovery of the atomic nucleus. To do this, you let alpha particles (charge: +2e mass: 6.64 × 10^27 kg) with a kinetic energy of 5.40 MeV impinge upon a gold foil. The alpha particles are repelled from the gold nuclei.

(a) What is the initial velocity of the alpha particle?
(b) How close can an alpha particle get to a gold nucleus before turning

around? (You can safely ignore the kinetic energy transferred to the gold nucleus)

Explanation / Answer

we know that

KE = (1/2)*m*v^2

v = sqrt (2*KE / m)

v = sqrt (2*5.40*10^6*1.6*10^(-19) / 6.64*10^(-27))

v = 1.61*10^7 m/s

(b)

point at which the alpha particle turn, velocity of particle is zero.

so KE = 0

KE converts into potential energy.

according to law of energy conservation,

PEi + KEi = PEf + KEf

let the distance b/w alpha particle and gold nucleus = r

0 + 5.4*10^6*1.6*10^(-19) = k*q1*q2 / r + 0

8.64*10^(-13) = 9*10^9*2e*79e / r

by solving,

r = 4.2*10^(-14) m

answer

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