Question

Uncertainty in position of a particle of 25 g in space is 10^–5 m. Hence, uncertainty in velocity (m s^–1) is (Planck’s constant, h = 6.6 × 10^–34 Js)

(a) 2.1 × 10^–28 (b) 2.1 × 10^–34 (c) 0.5 × 10^–34 (d) 5.0 × 10^–24

Answer 1

Correct option is (a) 2.1 × 10^–28  

Explaination::

mass=25g=25\(\times 10^{-3}\) kg , Δx=10⁻⁵m 

According to Heisenberg uncertainty principle

\(\triangle x.m.\triangle v=\frac{h}{4\pi}\)

\(\therefore \triangle v=\frac{h}{\triangle x.m.4\pi}\)

\(\frac{h}{4\pi}=5.272859 × 10^{-35}\) -{plancks constant / 4 π} 

\(\therefore \triangle v=\frac{5.272859 × 10^{-35}}{25\times 10^{-3}\times10^{-5}}\)

\(\therefore \triangle v= 2.1 \times 10^{-28}\) m s^-1