Question

According to De Broglie’s concept, the circumference of each electron of which must be equal to:
A.Diameter of an electron
B.The wavelength of an electron
C.The integral number of electron wavelength
D.Planck’s Constant divided by 2

Answer 1

Hint: A scientist named Louis de Broglie proposed a concept that stated that matter behaves like a wave. He then postulated a concept known as matter waves. To explain it in simpler terms, de Broglie believed that matter too exists in the form of a wave, and that all matter has a certain designated wavelength, in the boundaries of which it exists.

Complete step by step answer:
Before we move forward with the solution of this question, let us understand a few basic important concepts.
He supported his idea by stating that if light exists in the form of waves and particles (photons), then matter too must exhibit such dual nature of existence. He associated all matter with its own wavelength in the form of an equation known as the de Broglie’s wavelength. This equation establishes a relation between the wavelength of the matter and its momentum. Both these quantities are inversely proportional. This relation is equated using a constant known as Planck’s constant. Mathematical representation of this equation can be given as follows:
 \[\lambda = \dfrac{h}{p}\]
Where, \[\lambda \] is the wavelength, h is Planck’s constant and p is the momentum.
Several relations are deduced from this theory. One of them is known as de Broglie’s concept. This establishes a relation between the wavelength of the body and the circumference of movement. It is given by:
 \[2\pi r = n\lambda \] , where n is a constant and r is the radius value
Hence, according to De Broglie’s concept, the circumference of each electron of which must be equal to the integral number of electron wavelength

Hence, Option C is the correct option.

Note:
Matter waves were first experimentally confirmed to occur in George Paget Thomson's cathode ray diffraction experiment and the Davisson-Germer experiment for electrons, and the de Broglie hypothesis has been confirmed for other elementary particles.