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A beam of electrons of 25 e³Õkinetic energy is directed at a single slip of 2.0 μm width, then detected at a screen 4m beyond the slit. How far from a point directly in the line of the beam is the first location where no electrons are ever detected?

Short Answer

Expert verified

The line of the beam is detected aty=0.25mm

Step by step solution

01

 Step 1: Given information

The potential difference for the electron beam is25 e³Õ

The slit's width=2‰Ӿ
The space between the screen and the slit=4″¾

02

Concept Introduction

The wavelength of any moving charged particle is given by the,

λ=h2mqV…â¶Ä¦â¶Ä¦â¶Ä¦â¶Ä¦â¶Ä¦â¶Ä¦..(1)

Where m, q, and V are the mass, charge, and applied potential difference.

03

Calculation of the wavelength

Substitute the given information in equation (1) to obtain the wavelength such that,

λ=6.63×10−34 J⋅s2×(9.1×10−31 kg)×(1.6×10−19 C)×(25 V)=2.46×10−10 m

04

 Another formula substituting.

mλ=Ӭsinθ12λ=Ӭ×yD12×2.46×10-10 m=2.0×10−6 m×y4 my=0.25 mm

Therefore, the result is y=0.25 mm.

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