Question

In the Rutherford Gold Foil experiment, alpha particles (with a charge of 2e and a mass of 6.645x1027 kg) were shot directly at a thin sheet of gold with ht t but of the time t sometimes they would bounce directly back. The alpha particle would only bounce back when its path was aimed directly at a gold nucleus (otherwise it would pass through the empty space between nucle atom (rather than spread out even through the atom What is the closest distance that this alpha particle could get before bouncing back?0-1 incorect. Tries 1/5 Previous Tries Thie disesiceinn is closed Send Feedback

Answer 1

Kinetic energy of an alpha particle which is given by -

K.E = (1/2) m v²

where, m = mass of an alpha particle = 6.645 x 10^-27 kg

v = speed of an alpha particle = 1.287 x 10⁷ m/s

then, we get

K.E = [(0.5) (6.645 x 10^-27 kg) (1.287 x 10⁷ m/s)²]

K.E = 5.50 x 10^-13 J

What is the closest distance that this alpha particle could get before bouncing back?

we know that, P.E = K.E

k_e q₁ q₂ / d = K.E

where, q₁ = charge on an alpha particle = 2e = 2 x 1.6 x 10^-19 C

q₂ = charge on gold nucleus = Z p = 79 x 1.6 x 10^-19 C

k_e = proportionality constant = 9 x 10⁹ Nm²/C²

then, we get

d = [(9 x 10⁹ Nm²/C²) (2 x 1.6 x 10^-19 C) (79 x 1.6 x 10^-19 C)] / (5.50 x 10^-13 J)

d = [(3.64032 x 10^-26 Nm²) / (5.50 x 10^-13 J)

d = 6.61 x 10^-14 m