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The de-Broglie wavelength of an electron in motion is given by λ = h / p. Based on the relationship dλ / λ = - dp / P, if 0.5 equals P / 100 and P' is 200 times P, determine how the wavelength changes.

1. λ is inversely proportional to P
2. λ is directly proportional to P
3. λ is proportional to the square root of P
4. None of these relationships are correct

Correct answer: λ is inversely proportional to P

Solution

The de-Broglie wavelength is inversely proportional to momentum (λ ∝ 1/P). This relationship is derived from λ = h/p, where h is Planck's constant. The given equation dλ/λ = -dp/P also confirms this inverse proportionality.

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