Problem 11: An electron is accelerated through a potential difference of 50 V. Calculate its de Broglie wavelength.

Solution

Given: Applied potential difference, V = 50 V
Given particle = electron with charge, e = 1.6 × 10^{-19} C

Find: De Broglie wavelength, λ

According to de Broglie’s hypothesis, all matter exhibit both matter and wave characteristics. The wavelength of the associated wave is λ = h/mv. … (A)

Where v is the velocity of the particle.

Now we find the momentum, mv, of the electron as it is accelerated through the given potential difference of 50 V. We know that,

Here v is the velocity of the electron. Simplify this equation to get mv.

Substitute the values

Now put this value in the main de Broglie equation given above,

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