Question

What is the uncertainty in location of a of
photon of wavelength 5000 angstromn
if wavelength is known of accuracy one
picometre


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Answer 1

Answer ⇒ Δx ≥ h/2400π

Explanation ⇒ For an Photon, we know,

λ = h/p

where p is the momentum.

• Wavelength varies as inverse of momentum.
• But in case of error, the relative error in wavelength is equal to relative error in momentum.

∴ Δλ/λ =  Δp/p

∴ Δp = Δλ/λ × p

∴ Δp = 10⁻¹²/(5000 × 10⁻¹⁰)  × (mc)

∴ mΔv = 0.2 × 10⁻⁵ × mc

∴ Δv = 2 × 10⁻⁶ × c

∴ Δv = 2 × 10⁻⁶ × 3 × 10⁸

∴ Δv = 600

Thus, error in velocity is 600 m/s.

Now, using Heisenberg Uncertainty principle,

 Δx × Δv ≥ h/4π

∴ Δx ≥ h/4π × 600

∴ Δx ≥ h/2400π  m.