Rutherford's atom experiment problem

[Dana Fishel]

Homework Statement

In 1911, Ernest Rutherford discovered the nucleus of the atom by observing the scattering of helium nuclei from gold nuclei. If a helium nucleus with a mass of 6.68

10^-27 kg, a charge of +2e, and an initial velocity of 1.30

10^7 m/s is projected head-on toward a gold nucleus with a charge of +79e, how close will the helium atom come to the gold nucleus before it stops and turns around? (Assume the gold nucleus is held in place by other gold atoms and does not move.)

Homework Equations

electric field equations involving k constant, charge, mass, and velocity

The Attempt at a Solution

I was told by a classmate that this should work:

d = (9e9)4(79)(1.602e-19)^2 / (6.68e-27)(1.3e7)
= 8.4e-7 meters
(where e means x10^#)

But it's wrong, and I'm not sure which equation this solution came from in the first place.

 

[haruspex]

d = (9e9)4(79)(1.602e-19)^2 / (6.68e-27)(1.3e7)

It's not reasonable to expect others to decode that by reverse engineering the numbers.
Please post it as an equation using symbols, preferably defining them.

 

[andrevdh]

Think energy.

 

[BvU]

Haru is absolutely right. But you yourself can easily do the reverse engineering, isn't it ?

d = (9e9)4(79)(1.602e-19)^2 / (6.68e-27)(1.3e7)​

I see a k_coulomb, q₁, q₂, m, and a v. In short: all you need.
But dimensionally it doesn't fit. Andrev's hint should be enough to discover the little thingy that's still missing from your friendly classmate's spoiler !

[warning]: make sure you learn from this. Getting the answer from a mate means that in fact you miss the exercise. You can't have someone else train for the marathon in your place and still expect to be able to run it yourself!

 

[andrevdh]

It's very similar to throwing a ball upwards, except in this case the force increases drastically "upwards".