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 × 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) 80 kg ms⁻¹
(c) 8.0 × 10⁻²⁶ kg ms⁻¹ (d) 5.0 × 10⁻²⁶ kg ms⁻¹

Answer 1

The minimum

uncertainty in the measurement of the momentum of the

helium atom is

(a) 50 kg ms⁻¹

Answer 2

The minimum uncertainty in the measurement of the momentum of the helium atom is equal to 5.0 × 10⁻²⁶ kg ms⁻¹.

• According to Heisenberg's uncertainty principle, Δx.Δp≥h/4π.
• So,for a given uncertainty in position the minimum uncertainty in momentum is equal to h/4πΔx , which is a constant.
• Therefore , the minimum uncetainty in momentum for helium is same as that for an electron foe same uncertainty in their positions.