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an electron is alowed to move freely in a closed cubic box of length side 10 cm.tha maximum uncertainity in its velocity will observed as

an electron is alowed to move freely in a closed cubic box of length side 10 cm.tha maximum uncertainity in its velocity will observed as 
 

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1 Answers

Chetan Mandayam Nayakar
312 Points
10 years ago

the electron wave function is Ψ(x,y,z)=Csin(lπx/a)sin(mπy/a)sin(nπz/a), a=10cm, C is a constant such that                     ∫∫∫lΨ(x,y,z)l2dx dy dz =1,x=0 to a, y=0 to a and z=0 to a. px=(Melectron)vx=±lh/2a,py=±mh/2a,pz=±nh/2a

(px uncertainty)^2 =(average((px)^2))-(average(px))^2 = (average((px)^2))=(lh/2a)^2,similarly we have (mh/2a)^2 for y-component and (nh/2a)^2 for z-component.

l,m and n are natural numbers. you can easily see that as l,m and n go to infinity, the uncertainty also tends to infinity, which is the maximum uncertainty. However, the uncertainty is MINIMUM when l=m=n=1

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