Question

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

• A. $50kgm{s}^{-1}$
• B. $80kgm{s}^{-1}$
• C. $8.0\times {10}^{-26}kgm{s}^{-1}$
• D. $5.0\times {10}^{-26}kgm{s}^{-1}$
  

Answer 1

The correct option is D $5.0\times {10}^{-26}kgm{s}^{-1}$

Heisenberg's uncertainty principle states that the position and the momentum of a sub-atomic particle cannot be determined simultaneously.

The mathematical form of the uncertainty principle is stated as :

$\Delta x\times \Delta p\ge \frac{h}{4\pi }$

where,

$\Delta x=$ position of a sub-atomic particle

$\Delta p=$ momentum of the sub-atomic particle

$h=$ Planck's constant

In the given question, electron is the sub-atomic particle.

Given,

Position of an electron and a helium atom $=1nm$

The momentum of the electron $=5.0\times {10}^{-26}kgm{s}^{-1}$

When the position of an electron and a helium atom is same, and the momentum of the electron is known, then the momentum of the helium atom will be same as the momentum of the electron.

Therefore, the momentum of the helium atom is $5.0\times {10}^{-26}kgm{s}^{-1}$.

Hence, option (D) is correct.