Question

The position of both, an electron and a helium atom is known within 1.0 nm. Further the momentum of the electron is known within $5.0 \times 10^{- 26} \, \text{kgms}^{- 1} .$ The minimum uncertainty in the measurement of the momentum of the helium atom is

• A. $6.0\times 10^{- 26 \, }$ $kgms^{- 1}$
• B. $60$ $kgms^{- 1}$
• C. $50$ $kgms^{- 1}$
• D. $5.0\times 10^{- 26}$ $kgms^{- 1}$

Answer 1

Answer: (D)

According to uncertainty principle the product of uncertainty in position and uncertainty in momentum is constant for a particle.
i.e., $\Delta x\times \Delta p=\frac{h}{4 \pi }$
As $\Delta x=1.0$ nm for both electron and helium atom, so $\Delta p$ is also same for both the particle.
Thus, uncertainty in momentum of the helium atom is also $5.0\times 10^{- 26}kgms^{- 1}$ .