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The observable universe is ~93 billion light-years across — and it's still expanding.
Which of the following figure represents the variation of particle momentum and the associated de Broglie wavelength?
medium
Dual Nature of Radiation and Matter
2015
physics
Explanation To solve this problem, we need to understand the relationship between momentum ( P ) (P) ( P ) and the de Broglie wavelength ( λ ) . (\lambda). \\
\\
( λ ) . The de Broglie wavelength is given by the formula: λ = h P \\
\lambda = \frac{h}{P} \\
λ = P h
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where
is Planck's constant and
is the momentum of the particle.
From the formula, we can see that
is inversely proportional to
This means that as the momentum increases, the wavelength decreases, and vice versa.
Let's analyze the options:
• Option 1: The graph shows an increasing curve, which suggests that as
increases,
also increases. This is incorrect.
• Option 2: The graph shows a linear decrease, which suggests a direct inverse relationship. This is correct.
• Option 3: The graph shows a decreasing curve, which suggests that as
increases,
decreases. This is also correct.
• Option 4: The graph shows an increasing linear relationship, which is incorrect.
The correct graph should show a decrease in
as
increases, which is represented by Option 3.
Therefore, the correct option is Option 3.