Answer
Particle 1.
Work Step by Step
Let’s break this down in simpler terms:
The particle whose speed we know most accurately has the smallest uncertainty in its velocity. "Uncertainty" here means how much we’re unsure about a certain measurement. So, if we are really sure about the particle's speed, there's very little "uncertainty" in that speed.
Since the three particles have the same mass, the one with the smallest uncertainty in its velocity also has the smallest uncertainty in its momentum. Momentum is just mass multiplied by velocity, so if velocity is well-known, momentum is well-known as well.
Now, according to the uncertainty principle $ \Delta x \Delta p \geq \dfrac{\hbar}{2}$, there’s a competition between how well we can know the position $ \Delta x$ of a particle and how well we can know its momentum $\Delta p$. If we know one of these very accurately, we will know less about the other.
In this case, the particle with the smallest uncertainty in its momentum (the one we know its momentum the best) will have the largest uncertainty in its position. This means we can’t determine exactly where it is, it spreads out over a larger area.
From the given graphs, we can see that is $\bf particle\; 1$, whose wave function is wider and more spread out.
But for particles 2 and 3, their position uncertainty is smaller, meaning their wave functions are more squeezed together. This also means that we are more sure about their positions but less sure about their momentum and hence their velocities.
