please explain why the answers are b and e step by step The next two questions p

Question

please explain why the answers are b and e step by step

The next two questions pertain to the situation described below. Calcium atoms mass =666 x1026kg, assumed tobe indistinguishable, areth 50nm, separatedcted stinguishable, are cooled to a velocity m/s, and then directed one by one onto two 200 nm (between their centers). On a screen 4 meters away, the atoms are m at a point directly across from the midpoint of the two slits. nanofabricated slits, each of width te most likely toparated by Slits close-up 50 nm Ca atom 200 n 4 m 19) What is the minimum transverse distance on the screen so that the probability to detect the atoms is actually zero? a. 19.9 cm b. 9.9 cm c. 0 cm 20) Excitation l excited All Ca atoms in nd state None excited Now we change the experiment in the following way: We focus a laser onto a small spot that ONLY interacts with atoms passing through the top slit, The wavelength of the laser is such that it excites any atom that passes through the spot from the ground state to a highly excited state (for simplicity assume that any such atom stays in the excited state until the atom reaches the detection screen) Now what is the minimum transverse distance on the screen so that the probability to detect the atoms is actually zero?- a. 0 cm b. 10 cm c. 125 nm d. There is no such point- at every point on the screen there will always be some possibility to find the atoms. e. 80 cm Page 8 of 10

Explanation / Answer

1. The distance of the dark band from the center of the screen is given by:

y = (m+.5)*wavelength*D/d

D= distance of screen from slit, d = separation between the slits

m= order=0 in this case.

wavelength = de broglie wavelength = h/p= h/mv, h = 6.62e-34, m=6.66e-26, v=1

D=4 m , d = 200 e-9 m,

Using these values, y = 9.9 cm

2. For destructive interference due to single slit:

wavelength = 9.99 nm

sin(theta) = wavelength /slit width = .12

tan(theta) = sin(theta) = .12 = y/Distance of screen

So, y = .12 * 4 m = 80 cm

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.