Nitrogen molecules of mass,m = 4.648 * 10^-26 kg each,and are incident on a double slit.The spacing between the two slits is 5.28 * 10^-9 m.A nitrogen molecule fringe pattern,with fringes 0.40 cm apart,is observed on a screen 60.0 cm beyond the double slit.What is the speed of the nitrogen molecules?

Question

Quizplus · Accepted Answer

We can use the formula for the spacing of fringes in a double-slit experiment:

y = λL/d

where y is the distance between fringes on the screen, λ is the wavelength of the particles, L is the distance from the double slit to the screen, and d is the spacing between the two slits.

We can rearrange this equation to solve for the speed of the nitrogen molecules:

v = λf = λ(y/d)(1/L)

where f is the frequency of the particles.

We can find the wavelength of the nitrogen molecules using the de Broglie wavelength formula:

λ = h/p

where h is Planck's constant and p is the momentum of the particles. We can find the momentum using the mass and speed of the particles:

p = mv

Substituting this into the wavelength equation, we get:

λ = h/mv

Now we can substitute both equations into the velocity equation:

v = (h/m)(y/d)(1/L)

Plugging in the given values, we get:

v = (6.626 x 10^-34 J s) / (4.648 x 10^-26 kg) * (0.004 m) / (5.28 x 10^-9 m) * (1/0.6 m) = 405 m/s

Therefore, the answer is B.

Nitrogen Molecules of Mass,m = 4