Question

1.You measure the velocity of an electron to an accuracy of ±22.6 m/s. What is the minimum uncertainty in its position? (h = 6.626 × 10-34 J ∙ s, melectron = 9.11 × 10-31 kg)

A 32.2 μm

B4.03 μm

C5.12 µm

D 8.05 μm

E16.1 μm

2.A 10-g bouncy ball is confined in a 8.3-cm-long box. What is its minimum energy? (h = 6.626 × 10-34 J ∙ s)

A.8.1 × 10-65 J

B.9.4 × 10-75 J

C.3.2 × 10-46 J

D.1.3 × 10-20 J

Answer 1

1)
The uncertainty in the velocity of the electron is
  
And the mass of the electron is
  
So, from the uncertainty relation, we write
   
So, the uncertainty in the position is
   

So, putting the given values, we get
  
  
   
So, the minimum uncertainty in the position is
  
So, option (C) is correct.

2)
The uncertainty in the position is
     
So, the uncertainty in the momentum is given by
   
  So, we get
  
  
So, if the uncertainty in the momentum is assumed to be of the order of the momentum itself, then, we get the minimum value of the momentum

  So, the minimum energy is
  
  
So, option (A) is correct.