Question

b) Calculate the kinetic energy associated with a moving electron
having de Broglie wavelength of 725 nm.
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Answer 1

Given:

The moving electron  has  the de Broglie wavelength of 725 nm.

To find:

Calculate the kinetic energy associated with a moving electron  having de Broglie wavelength of 725 nm.

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Solution:

From given, we have,

The moving electron  has  the de Broglie wavelength of 725 nm.

The formula used to calculate the de Broglie wavelength is given as follows.

λ = h/mv

λ² = h²/m²v²

λ² = h²/2m(KE)

As the kinetic energy is given by the formula, KE = 1/2 mv²

Now substitute  the given values in the above equation

[725 × 10^{-9}]² = (6.6 × 10^{-34})² / [2 × 9.1 × 10^{-31} × KE}

upon solving the above equation, we get,

KE = 4.55 × 10^{-25}

KE = 4.55 × 10^{-25} / 1.6 × 10^{-19}

KE = 2.84 × 10^{-6} eV

Therefore, the kinetic energy associated with a moving electron  having de Broglie wavelength of 725 nm is 2.84 × 10^{-6} eV