Calculate the uncertainty in the momentum of an electron if it is confined to a linear region of length 1 × 10-10 metre.

Question

Calculate the uncertainty in the momentum of an electron if it is confined to a linear region of length 1 × 10-10 metre. (A) 5.37 × 10-27 kg m s -1 (B) 5.27 × 10-25 g m s -1 (C) 5.37 × 10-25 g m s -1 (D) 5.27 × 10-25 kg m s -1

Tardigrade Admin · Accepted Answer

According to uncertainty principle, Δ x ⋅ Δ p=(h/4 π) or Δ p=(h/4 π Δ x) Δ p=((6.626 × 10-34 kg m 2 s -1)/4 × 3.14 ×(10-10 m ))=5.27 × 10-25 kg m s -1

Q. Calculate the uncertainty in the momentum of an electron if it is confined to a linear region of length $1 \times 1 0^{- 10}$ metre.

$5.37 \times 1 0^{- 27} k g m s^{- 1}$

$5.27 \times 1 0^{- 25} g m s^{- 1}$

$5.37 \times 1 0^{- 25} g m s^{- 1}$

$5.27 \times 1 0^{- 25} k g m s^{- 1}$

According to uncertainty principle,

$Δ x \cdot Δ p = \frac{h}{4 π}$ or $Δ p = \frac{h}{4 π Δ x}$

$Δ p = \frac{( 6.626 \times 1 0 ^{- 34} k g m ^{2} s ^{- 1} )}{4 \times 3.14 \times ( 1 0 ^{- 10} m )} = 5.27 \times 1 0^{- 25} k g m s^{- 1}$

Q. Calculate the uncertainty in the momentum of an electron if it is confined to a linear region of length 1×10−10 metre.

5.37×10−27kgms−1

5.27×10−25gms−1

5.37×10−25gms−1

5.27×10−25kgms−1