numericals for Hinesberg uncertainty principal

Numerical

1. calculate uncertainty in velocity of an electron if uncertainty in position is  1Angstrom given mass of electron 9.1× 10^-34kgm^2s^-1.

sol.

 ∆x = 10^-10m

 mass of electron = 9.1×10^-31kg

h =6.6×10^-34kg m^2s^-1

∆V=? 

 we know ∆x.∆p=h/4π

∆xm∆V =h/4π        because p=mv

or ∆V= h/(4π×m×∆x) 

putting all values we get 

∆V= 5.77×10^5m/s      ans




2. calculate uncertainty in position of electron if uncertainty in velocity is   0.0001℅ given 
velocity of electron = 300m/s.

sol.

∆x =? 
 ∆v= 0.0001℅×300
      = (0.0001/100) ×300= 3×10^-4m/s

mass of electron = 9.1×10^-31kg

h =6.6×10^-34kg m^2s^-1

we know ∆x.∆p= h/4π
      
       ∆x.m.∆V= h/4π
       
      ∆x= h/(4π.m.∆V) 

putting all value we get  

∆x= 1.92×10^ -3metre           ans