Show that if the measurement of the uncertainty in the location of the particle is equal to its de Broglie wavelength,the minimum uncertinty in its velocity (/_\v) is equal to 1/4pi of its velocity(V)

Show that if the measurement of the uncertainty in the location of the

1.	Show that if the measurement of the uncertainty in the location of the particle is equal to its de Broglie wavelength,the minimum uncertinty in its velocity (/_\v) is equal to 1/4pi of its velocity(V)
Answer» Solution :If, uncertainty in position`=/_\x=gamma`,the vale of uncertainty in velocity=`v/(4PI)` Heisenberg.s PRINCIPLE states that `/_\x./_\v.m=h/(4pi)`………….(i) de Broglie equation states that `gamma=h/(mv)`………..(2) `:.h=gamma.m.v`……..(3) `/_\x=h/(/_\v.4pi)`.............(4) `/_\X=(gammaxxm.v)/(/_\v.4pi.m)` `if/_\x=gamma` `/_\v=(CANCEL(x.m).v)/(cancel(x).4pi.cancel(m))=v/(4pi)`.