Kinetic energy of an electron which is associated with de Broglie's wavelength 20 angstrom is - (a)1.0eV (b)1.51eV (c)0.59eV (d)0.38eV.

By Ritesh|Updated : November 9th, 2022

The kinetic energy of an electron which is associated with de Broglie's wavelength 20 angstrom is 0.38 eV. Steps to find the de Broglie's wavelength 20 angstrom:

Given that λ = 20 Å = 20 x 10-10 m

We know that λ = h/mv

On rearranging we get mv = h/λ

Squaring on both sides:

(mv)2 = h2/λ2

Dividing the above equation by 2m we get:

(mv)2/2m = h2/λ22m

½ mv2 = h2/λ2 x 2m

Substituting the values we get:

= (6.6 x 10-34)2/ (20 x 10-10)2 x 2 x (9.1 x 10-31)

= 6 x 10-20 J

In simplification we get:

= 6 x 10-20/ 1.6 x 10-19 eV

= 0.38 eV

De-Broglie Waves

It is claimed that matter possesses both a wave and a particle-like character. De Broglie waves are the characteristics of a material entity that vary in time or space while acting in a manner like waves. They are named after the discoverer Louis de Broglie. Additionally known as matter-waves. It is very similar to the dual nature of light, which exhibits both wave and particle behavior and has been demonstrated experimentally.

Louis de Broglie, a physicist, postulated that particles might possess both particle and wave qualities. To support Louis de Broglie's hypothesis, the experimental detection of the wave character of electrons was also made. We do not perceive the wavelengths of the everyday items we view as waves since they are very little and invisible. De Broglie wavelengths can be clearly seen in the case of subatomic particles, though.

de Broglie Wavelength for Electrons

De Broglie waves occur as a closed loop when electrons orbit atoms' nuclei, which means they can only exist as standing waves and fit evenly around the loop. This condition causes the electrons in atoms to orbit the nucleus in specific arrangements, or states, known as stationary orbits.

Summary:

Kinetic energy of an electron which is associated with de Broglie's wavelength 20 angstrom is - (a)1.0eV (b)1.51eV (c)0.59eV (d)0.38eV.

An electron's kinetic energy at wavelength 20 angstrom, the de-Broglie wavelength, is 0.38 eV. de Broglie wavelength is similar to the dual nature of light which shows both particle and wave-like behavior.

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