Can a Single Point Grapefruit Create an Interference Pattern?

[stuDYING]

Homework Statement

Even a grapefruit has a de Broglie wavelength.

If the grapefruit is thrown with a speed of 8 m/s toward a wall with two holes separated by 0.6 m, find the angular separation between successive maxima of the resulting interference pattern. Treat the grapefruit as point-like and assume its mass is 0.6 kg. Planck’s constant is 6.62607 × 10^−34 J · s. Answer in units of radian.

Relevant Equations

lambda = h/p

I tried using lamba = h/p as follows:

(6.626 * 10^-34 J *s) / (8 m.s * 0.6 kg) = 1.38041667*10^−34

and then using the small angle approximation sin(alpha) = lamba/d as follows:

(1.38041667*10^−34)/(0.6m) = 2.30069444 * 10^−34

then converting to radians with the following:

(2.30069444 * 10^−34) * (pi/180) = 4.01546931* 10^−36

However, this answer is none of the answer choices so I did something wrong. I think I might have not been supposed to use the small angle approximation but I'm not sure if that's the only thing and if so how to fix it.

 

[osilmag]

Hey there. I think you converted the $sin(\alpha)$ into radians, not the actual angle $\alpha$. How do you change $sin(x)$ to $x$.?

 

[stuDYING]

Hey there. I think you converted the $sin(\alpha)$ into radians, not the actual angle $\alpha$. How do you change $sin(x)$ to $x$.?

Oh gosh I'm so dumb sometimes. You're completely right - thank you so much!

 

[kuruman]

I don't mind preposterous problems, but I do mind nonsense problems that try to be cute but actually undermine what is to be reinforced. It's OK to suspend disbelief and go along with the gag of a "point" 0.6-kg grapefruit. However, the question asserts that there is a "resulting interference pattern." Huh? That's not OK. A single point grapefruit does not make an interference pattern; it makes a single (point) splat on the observation screen.

One needs to use many many point grapefruits to see the interference pattern eventually emerge on the screen, in this case as streaks of grapefruit juice. The gradual emergence of the interference pattern, one particle at a time, has been experimentally verified with low-intensity interference experiments. Whether you believe that a photon interferes with itself or not, when it hits that screen and you measure its position BAM! it collapses to a point in space where the probability of being there is high. This question promotes the wrong picture that a single particle generates a complete interference pattern and that one observes on the screen a superposition of identical patterns, each produced by a single particle. Tsk! Tsk! Tsk!