Question

According to the wave-particle duality of matter by de-Broglie, which of the following graph plot presents most appropriate relationship between wavelength of electron () and momentum of electron (p)?

• A.

  

• B.

  

• C.

  

• D.

  

Answer 1

The Correct Option is A

By de-Broglie relation:

\[ \lambda = \frac{h}{p} \quad \text{(where \(h\) is Planck’s constant)} \]

This represents an inverse relationship between \(\lambda\) and \(p\), resulting in a rectangular hyperbola.

Answer 2

The relationship between the wavelength of an electron (\(\lambda\)) and its momentum (\(p\)) is given by the de Broglie equation, which is expressed as:

\(\lambda = \frac{h}{p}\)

where \(h\) is Planck's constant.

According to this equation, the wavelength \(\lambda\) is inversely proportional to the momentum \(p\). As momentum increases, the wavelength decreases, and vice versa. This relationship is represented graphically as a hyperbola, where one variable is inversely proportional to the other.

Upon analyzing the given options, the graph that most appropriately depicts the inverse relationship between \(\lambda\) and \(p\) is represented by a hyperbolic curve. Below is the correct graphical representation:

This graph illustrates that as the momentum (\(p\)) of the electron increases, its wavelength (\(\lambda\)) decreases, complying with the inverse relationship stated by the de Broglie hypothesis.