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Fundamentals Of Physics
Found in: Page 1181

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Short Answer

Figure 38-24 shows an electron moving through several regions where uniform electric potentials V have been set up. Rank the three regions according to the de Broglie wavelength of the electron there, greatest first.

The rank is λ2>λ1>λ3.

See the step by step solution

Step by Step Solution

Step 1: Describe the de Broglie wavelength:

The de Broglie wavelength is given by,


Here, h is the Planck's constant, λ is wavelength, and p is the momentum.

The kinetic energy in terms of momentum is given by,

role="math" localid="1663142299185" K=p22mp=2mK

Here, m is the mass.

Consider an electron, accelerated with a potential difference of V, the kinetic energy is given by,

K = eV

The momentum is given by,


The expression for wavelength will be as follows:


Step 2: Rank the three regions according to the de Broglie wavelength of the electron:

From the above de Broglie wavelength expression, the wavelength is inversely proportional to the V, which means the wavelength decreases as the potential difference increases and vice-versa.

As given the potential difference,

V1=-100 VV2=-200 VV3=+100 V

So, the rank of de Broglie wavelength will be λ2>λ1>λ3 .

Therefore, the rank is λ2>λ1>λ3 .

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