A) Bullets of mass 1.74 gm are fired in parallel paths at speeds of 206.8 m/s th

Question

A) Bullets of mass 1.74 gm are fired in parallel paths at speeds of 206.8 m/s through a 2.20 mm diameter hole. How far from the hole must you be, in order to detect a 1.83 cm spread in the beam of bullets?


B) Data collected from the Wilkinson Microwave Anisotropy Probe (WMAP) show that the Big Bang occurred 13.7 billion (= 13.7 x 109 ) years ago. How far will a photon of light travel in space in 13.7 billion years?


Hint: The idea behind this problem is that because of the wave-particle duality, the stream of bullets can also be viewed as a wave with an incredibly small wavelength. The problem is solved by considering single slit diffraction through the hole. You will find that in order to detect a 1.83 cm spread in the beam of bullets, you need to be farther from the hole than the size of the known cosmos.

*I have tried 1.56x10^28m for A and 1.30x10^23km for B and it gets marked wrong.

Explanation / Answer

the wavelength for a particle is given by

wavelength = h/mv = 6.626x10^-34 / 0.00174 * 206.8 =

= 18.414 x 10^-34

Now... diffraction from a circular opening is

D y / L = 1.22 * wavelength

The "spread" is actually 2y, so in your case y = 0.915 cm = 0.00915 m

You are asked to find L, the distance from you to the hole, so...

L = D y / 1.22 * wavelength = 0.0022 * 0.00915 / 1.22 * 18.414 x 10^-34 =

= 8.96 x 10^27 meters

(this is huge...)

Now for part b...

13.7 billion years = 4.32 x 10^17 seconds

multiply this by speed of light, 300000000 m/s and you get

distance =speed * time = 1.296 x 10^26 meters = 1.296 x 10^23 km

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