What reasoning led de-Broglie to put forward the concept of matter wave? The wavelength λ, of a photon, and de-Broglie wavelength associated with a particle of mass m has the same value, say λ. Show that the energy of photon is $\frac{2 λmc}{h}$ times the kinetic energy of the particle.

Solution

De-broglie reasoned that nature is symmetrical and that the two basic physical entities, matter and energy must have symmetrical character. This led him to put forward the bold hypothesis that moving particles of matter should display wave-like properties under suitable conditions. If radiation shows a dual nature, so should matter exhibit dual radiation.

Now, kinetic energy is given by,

K . E = \frac{P^{2}}{2 m} \Rightarrow P = \frac{h}{λ}

∴

K . E = \frac{h^{2}}{2 {mλ}^{2}}

Also, Energy of a photon =

\frac{hc}{λ}

∴

\frac{K}{E} = \frac{h}{2 mcλ}

\Rightarrow

E = \frac{2 mcλ}{h} . K .

For Daily Free Study Material Join wiredfaculty

Wave Optics

What reasoning led de-Broglie to put forward the concept of matter wave? The wavelength λ, of a photon, and de-Broglie wavelength associated with a particle of mass m has the same value, say λ. Show that the energy of photon is $\frac{2 λmc}{h}$ times the kinetic energy of the particle.

Some More Questions From Wave Optics Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction

For Daily Free Study Material Join wiredfaculty

Wave Optics

What reasoning led de-Broglie to put forward the concept of matter wave? The wavelength λ, of a photon, and de-Broglie wavelength associated with a particle of mass m has the same value, say λ. Show that the energy of photon is 2λmch times the kinetic energy of the particle.

Some More Questions From Wave Optics Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

What reasoning led de-Broglie to put forward the concept of matter wave? The wavelength λ, of a photon, and de-Broglie wavelength associated with a particle of mass m has the same value, say λ. Show that the energy of photon is $\frac{2 λmc}{h}$ times the kinetic energy of the particle.