De-Broglie’s Hypothesis | Chemistry Assignment Help

De-Broglie’s Hypothesis

The French physicist Louis de Broglie made a bold assertion in 1923. Considering Einstein's relationship of wavelength lambda to momentum p, de Broglie proposed that this relationship would determine the wavelength of any matter, in the relationship:

lambda = h / p Where h is Planck's constant and p is momentum .

This wavelength is called the de Broglie wavelength.


According to de Broglie, an electron of mass ‘m’ moving with a velocity ‘v’ should be associated with a wave having wave length (lambda). This wave length and velocity are related by the following mathematical equation =>

De-Broglie’s Hypothesis                                       …(1)

Chemistry Assignment Help Order Now Where h is the Planck’s constant and mv is the momentum of the moving particle. Equation is known as de Broglie relationship and can be written as

De-Broglie’s Hypothesis  or mv  µ De-Broglie’s Hypothesis                       …(2)

Equation (2) is another form of de Broglie relationship and this can be stated in words as “The momentum of a moving particle is inversely proportional to the wave-length of the waves associated with it.”

Proof of de Broglie Equation

Let us first consider the case of a photon. If we consider it to be a wave of frequency n, its energy is given by

E = hn …(3)

If we now consider it as a particle of mass m, its energy is given by

E = mc2 …(4)

From equation (3) and (4), we get

hn = mc2 …(5)

As the photon travels in free space with velocity of light c, its momentum p is given by

P = mass ´ velocity  = mc …(6)

On dividing equation (5) by (6), we get

De-Broglie’s Hypothesis

or De-Broglie’s Hypothesis   [De-Broglie’s Hypothesis c = vl = Frequency ´ wave length]

or De-Broglie’s Hypothesis                          …(7)

de-Broglie assumed that the above relation holds good for material particles like electrons, and hence for electrons eq. (7) becomes as

De-Broglie’s Hypothesis                                     …(8)

Where m is the mass, v the velocity, l the wave length and p the momentum of an electron. Equation (8) is same as equation (1).

De-Broglie Relationship and Bohr’s Theory

Application of the de-Broglie’s relationship to a moving electron around a nucleus puts some restrictions on the size of orbits. It means that electron is not a mass particle moving in a circular path but is instead a standing wave train (non-energy, radiating motion) extending around the nucleus in the circular path as shown below:

De-Broglie Relationship and Bohr’s Theory

For the wave to remain continually in phase, the circumference of the orbit should be an integral multiple of wavelength l i.e.,

2pr = nl …(9)

Where r is the radius of the orbit and n is a whole number.

From equation (8), we get

l = h/mv …(10)

Substituting the value of l in equation (9), we get

de-Broglie Relationship and Bohr’s Theory  or  radiant energy                 … (11)

Which is the same as Bohr’s second postulate. From equation (11) it follows that “Electron can move only in such orbits for which the angular momentum must be an integral multiple of h/2p. If the circumference is bigger or smaller than the value as given by equation (11), it means that the wave is not in the phase as shown in figure(2). Thus, de-Broglie relation provides a theoretical basis for the Bohr’s second postulate.

Our Customer Service Support Center

Assignmenthelp.net's Services – ready to help students around the clock (24/7 technical support) Live Supports by Phone, Chat or E-mail (support@assignmenthelp.net). The assignments, we provide is plagiarism free and offer free download facility of Chemistry/Physics tutorials as well. Expert online chemistry tutors at Assignmenthelp.net provide all sorts of help regarding your problems in chemistry(de-broglie’s hypothesis, atomic structure) through e-mail and live chat.


To schedule a Chemistry (De-Broglie’s Hypothesis) tutoring session Click here
To submit Chemistry assignments Click here


Following are some of the topics in Chemistry (Atomic Structure, De-Broglie’s Hypothesis) in which we provide assignment/homework help:

Online Chemistry Help | Chemistry Assignment Help | Online Chemistry Help | Online Chemistry Tutor | Atomic Structure Help | Chemistry Homework Help | Chemistry Tutoring | Chemistry helper | Chemistry Homework Answers| Help With Chemistry Homework | Physical Chemistry Help | Chemistry Homework Assignment Help | Online Chemistry Tutoring Services Online Tutoring