Video Transcript
An alpha particle is fired toward a
fully ionized gold nucleus. The figure shows five possible
paths along which the alpha particle could initially move. For which path would the alpha
particle undergo the least deflection due to the gold nucleus?
Looking at our figure, we see here
the gold nucleus. And we’re told that this gold atom
is fully ionized. That is, all of its electrons are
stripped off. So there are no negative charges
here, only the positively charged nucleus. And then we have these five
possible pathways, path A, path B, C, D, and E, for an alpha particle to follow as
it approaches the nucleus. We want to know along which of
these five paths will the alpha particle be deflected least due to its interaction
with the gold nucleus.
To get a sense of what this
interaction will be like, let’s recall that an alpha particle is a helium
nucleus. That is, it consists of two
protons, we’ve drawn them here in blue, and two neutrons, we have them in green. So overall, an alpha particle has a
positive electric charge and so, we see, does our gold nucleus. Because these two objects have like
electrical charges, that means they’ll repel one another, push one another away.
What we’re going to assume though
is that because our gold nucleus is so much more massive than our much smaller alpha
particle, relative to the moving alpha particle, we’ll say that our gold nucleus is
stationary, fixed in place. So as our alpha particle travels,
potentially, all these different paths, it will move, but the gold nucleus will
not.
Let’s start looking at our path
options by considering path C. This path, if we follow it forward, leads directly to
the center of the gold nucleus. But as we think about the
interaction between an incoming alpha particle and that nucleus, we know that
physically the alpha particle will not reach the nucleus. The reason is that the closer the
alpha particle gets, the more strongly it will be repelled by an electrostatic
force, the coulomb force. So no matter how fast the alpha
particle is moving initially, that repulsion between it and the gold nucleus will
slow it down until eventually it comes to a stop. It will only be stopped for an
instant though. After that, it will start to move
back in the direction it came.
If we think about this motion in
terms of particle deflection, we can see that this is an extreme case. It wouldn’t be possible for the
alpha particle to be deflected more than it is here, where it goes in one way and
comes out 180 degrees opposite that. Path C, then, is an example of the
most deflection possible. And therefore, it won’t be our
answer for the path that undergoes the least deflection.
Now we saw that path C’s direction
was on axis with the center of the gold nucleus. But what if we move off of that
axis slightly? That is, what if we follow, say,
path B? In that case, our alpha particle
won’t come to a complete stop, because it’s not moving directly toward the nucleus,
but will instead be scattered or deflected. We see though that this deflection
is much less than that experienced by an alpha particle following path C. This is
because an alpha particle following path B is passing by the nucleus at a greater
distance. In fact, it’s generally true that
the more distance there is between our particle’s path and the gold nucleus, the
less that particle will be deflected.
We could show that this way. If we draw a line that passes right
through the center of the gold nucleus, since all five of our paths involve motion
that’s parallel to this blue line, then if we draw a line that’s perpendicular to
this horizontal blue one, the farther away from the blue line a particle’s path is,
the less that particle will be deflected as it follows that path. And that’s exactly what we want to
find. It’s the path that leads to the
least deflection of the alpha particle.
To figure out which of our five
paths this is, let’s extend this vertical line we’ve drawn a bit. And now we can pretend that it’s
the vertical axis of a graph. So this point right here will be
our origin. And then using a ruler, we’ll make
evenly spaced markings along this. Relative to these tick marks, these
markings, which we’ll leave without numbers or any units, let’s figure out where our
four remaining path candidates, paths A, B, D, and E, lie.
Starting at the top, we can see
that here is path A. That’s one, two, three, a little bit more than three tick marks
up away from our origin. Then right here, there’s where path
B crosses this vertical line. We can see that that’s less than
one tick mark. And then path D crosses it here,
which is slightly less than two tick marks away from our origin. In this case, whether we’re above
or below the origin doesn’t matter, only that total distance. And then path E, we see, intersects
this line here, at about two and a half tick marks from our origin. So of all five paths, path A is
farthest away from the origin. And that means an alpha particle
traveling this pathway will be farthest away from the gold nucleus and, therefore,
be deflected by that nucleus the least.
And so that’s our answer to this
question. An alpha particle following along
path A would undergo the least deflection of any of these path options.
