Question

the mass of an electron is 9.1 × 10^-31 kg. if its k.e is 3.0 × 10^-25 J, calculate its wavelength. structure of atom.​

Answer 1

Given :-

• Mass of electron = 9.1 × 10⁻³¹ kg.
• Kinetic energy of electron = 3.0 × 10⁻²⁵ J.

To Find :-

• Wavelength (λ) of the electron.

Solution :-

We are given that, K.E = 3.0 × 10⁻²⁵ J.

Also, $\rm{K.E=\dfrac{1}{2}mv^2{\implies}v=\left(\dfrac{2K.E}{m}\right)^{1/2}}$

Putting the given values, we get,

$\implies\rm{v=\left(\dfrac{2\times{}3.0\times{}10^{-25}\:kgm^2s^{-2}}{9.1\times{}10^{-31}\:kg}\right)^{1/2}}$

$\implies\rm{v=812\:ms^{-1}}$

$\rule{350}{3}$

According to de Brogile equation, $\rm{\lambda=\dfrac{h}{mv}}$

where:-

• Planck's constant, h = 6.626 × 10⁻³⁴ Js.
• Mass of electron, m = 9.1 × 10⁻³¹ kg. (given)
• Velocity of electron, v = 812 ms⁻¹ (found above)

Putting these values in the equation, we get,

$\implies\rm{\lambda=\dfrac{6.626\times{}10^{-34}\:kgm^2s^{-1}}{(9.1\times{}10^{-31}\:kg)(812\:ms^{-1})}}$

$\implies\rm{\lambda=8967\times{}10^{-10}\:m=}\:\bold{896.7\:nm.}$