Question

An electron is moving with a kinetic energy of 2.275 * 10 ^-25 J . Calculate its de broglie wavelength .

Answer 1

Given :-

• K.E of electron = 2.275 × 10⁻²⁵ J.

To Find :-

• de Brogile wavelength (λ) of the electron.

Solution :-

We are given that, K.E = 2.275 × 10⁻²⁵ J.

Also, K.E = 1/2mv²

where,

• Mass of electron, m = 9.11 × 10⁻³¹ kg.
• Velocity of electron, v = ?

Putting these values, we get,

$\implies\rm{2.275\times{}10^{-25}=\dfrac{1}{2}\times{}9.11\times{}10^{-31}\times{}v^2}$

$\implies\rm{v^2=\dfrac{2.275\times{}10^{-25}\times{}2}{9.11\times{}10^{-31}}}$

$\implies\rm{v^2=0.5\times{}10^6}$

$\implies\rm{v=0.7\times{}10^3\:ms^{-1}}$

$\hrulefill$

Now, we got velocity of the electron

Using de Brogile equation,

$\implies\rm{\lambda=\dfrac{h}{mv}}$

where,

• Planck's constant, h = 6.626 × 10⁻³⁴ kgm²s⁻¹.

We get,

$\implies\rm{\lambda=\dfrac{6.626\times{}10^{-34}\:kgm^2s^{-1}}{(9.11\times{}10^{-31}\:kg)(0.7\times{}10^3\:ms^{-1})}}$

$\implies\rm{\lambda=}\:\bold{1.04\times{}10^{-6}\:m.}$