Find the uncertainty in the position of an electron which is moving with a velocity of 2.99 10^4 ~cm ~s ⁻¹ , accurate up to 0.0016 % . (Given, m_e=9.1 10⁻²⁸ ~g , h=6.626 10⁻²⁷ erg.s)

Step-by-step solution

According to Heisenberg uncertainty principle, the product of uncertainties in position ( x) and velocity ( v) is always equal to or greater than h 4 . aligned & x m v h 4 & v=2.99 10^4 cms ⁻¹ & Uncertainty =0.0016 % & Uncertainty in velocity ( v)=2.99 10^4 0.0016 100 & =0.478 ~cm ~s ⁻¹ & x= h 4 m v & = 6.62 10⁻²⁷ Js 4 3.14 9.1 10⁻²⁸ ~g 4.78 10⁻¹ ~cm ~s ⁻¹ & =12.11 ~mm & aligned