If the radius of the 1st Bohr orbit in a hydrogen atom can be determined  with an uncertainity of 1% .What will be the minimum velocity of electron in that orbit ?
 
 Answer to the problem is 1.09*(10 power 8)m/s
 
please help as i cannot make anything out of the problem!

 

RADIUS OF THE FIRST BOHR ORBIT IS 0.53 ANGSTROM =0.53*(10^(-10))

 

BY HEISENBERG'S UNCERTAINITY PROBLEM WE KNOW THAT
 
  p*x >= h/(4(pie))--------(1)
 
  where p= momentum of the electron

        x= uncertainity in the location of Bohr orbit (1%= 10^(-2))

        h= planck's constant (6.62 * 10^(-34)) Js
 
 p can be expressed as m*v

        where m = mass of the electron ( m=9.1*10^(-31)kg)

              v= velocity of the electron

  putting the values in (1) we get  pie=3.14

 

v >=6.62*10^(-34)/[(4* 3.14)*9.1*10^(-31)*0.53*(10^-10)*10^(-2)]  

v >= 1.094 * (10^8) m/s

therefore the least value of velocity is 1.094 * (10^8) m/s  

 

with regards                                

The problem is based on Heisenberg's Uncertainty Principle which state that 'it is not possible to determine simultaneously both the position and momentum of an electron'. It is given by the formula-

p  *x  =h /4pie

where, p = momentum of the electron (mass of electron * velocity)

           x = uncertainty

            h= planck's constant

By putting the values, the velocity of the electron can be calculated.