Question

If the Kinetic energy of an electron is made 0.50 times then its de-Broglie's wavelength
would become
(A) 2.0 times (B) 1.41 times (C) 9 times (D) invariant​

Answer 1

Given:

The kinetic energy of an electron is made 0.50 times its original kinetic energy.

i.e. K.E.₂ = 0.50  K.E.₁

To find:

de-Broglie's wavelength of an electron =?

Step-to-step-explanation:

• The de Broglie's wavelength of an electron is given by:

       $\displaystyle \lambda = \frac{h}{\sqrt{2mE} }$

       where

       λ = de Broglie's wavelength

       h = Plank's constant

      m = mass of an electron

       E = kinetic energy of an electron

• From the above equation, it shows that de Broglie's wavelength of an electron is inversely proportional to the square root of the kinetic energy.

       $\displaystyle \lambda=\frac{1}{\sqrt{E} }$

• Now, we have to find the de Broglie's wavelength of an electron if the kinetic energy of an electron is made 0.50 times.

• Put E = 0.50 in the above equation

      $\displaystyle \lambda=\frac{1}{\sqrt{0.50} }$

      λ = 1.41

• Hence the Kinetic energy of an electron is made 0.50 times then its de Broglie's wavelength would become 1.41 times than the original.

Correct option is : (B) 1.41 times