Question

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

• A. $50 \,kg\, ms ^{-1}$
• B. $5.0 \times 10^{-26}\, kg \,ms ^{-1}$
• C. $80 \,kg\, ms ^{-1}$
• D. $80 \times 10^{-26} \,kg\, ms ^{-1}$

Answer 1

Answer: (B)

By Heisenberg's uncertainty principle
$\Delta x \times \Delta p \geq \frac{h}{4 \pi}$
when the position of electron and helium atom is same and momentum of electron is known within a range, therefore the momentum of helium atom is also equal to the momentum of electron, i.e.
$5 \times 10^{-26} \,kg\, m \,s ^{-1}$