Question

Two small slits are cut 0.2 mm apart in a small piece of metal. Many electrons are fired at the slits with a speed of 300 m/s . A detector is placed 5 m away on the other side of the slits.

Part A

What is the smallest distance from the central maximum that the detector will not see any electrons?

Part B

If we repeat the experiment with protons instead of electrons, what is the smallest distance from the central maximum that the detector will not see any protons?

Item 14 14 of 14 > Two small slits are cut 0.2 mm apart in a small plece of metal. Many electrons are fired at the sits with a speed of 300 m/s. A detector is placed 5 m away on the other side of the sits What is the smallest distance from the central maximum that the detector will not see any electrons 0 AED Omi? 7.3 Submit Previous Answers Request Answe Incorrect; Try Again; 6 attempts remaining if we repeat the experiment with protons instead of electrons, what is the smallest distance from the central m that the detector will not see any protons? imum

Answer 1

(a) Wavelength associated with the electrons, $\lambda$ = h/mv

So, $\lambda$ = 6.6*10^-34/9.1*10^-31*300 = 2.417*10^-6 m

Smallest distance from central maximum is equal to the fringe width which is given as = $\lambda$ D/d, where,

D = 5 m, d = 0.2*10^-3 m, hence, required distance,

s = 2.417*10^-6*5/0.2*10^-3 = 6.0425 cm

(b) Wavelength associated with the protons, $\lambda$ = h/mv

So, $\lambda$ = 6.6*10^-34/1.67*10^-27*300 = 1.317*10^-9 m

Required distance, s = 1.317*10^-9*5/0.2*10^-3 = 0.0329 mm