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)?
The Correct Option is A
Approach Solution - 1
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.
Approach Solution -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.
Top JEE Main Chemistry Questions
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)- At equilibrium the concentrations of and in a sealed vessel at . What will be for the reaction
- Find out the major products from the following reactions
Cobalt chloride when dissolved in water forms pink colored complex $X$ which has octahedral geometry. This solution on treating with cone $HCl$ forms deep blue complex, $\underline{Y}$ which has a $\underline{Z}$ geometry $X, Y$ and $Z$, respectively, are
- The correct order of atomic radii is:
Top JEE Main de broglie hypothesis Questions
Top JEE Main Questions
- In a hydrogen like atom, when an electron jumps from the $M$ - shell to the $L$ - shell, the wavelength of emitted radiation is $\lambda$. If an electron jumps from $N$-shell to the $L$-shell, the wavelength of emitted radiation will be :
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)- The value of is
- The number of terms of an is even. The sum of the odd terms is and of the even terms is . The last term exceeds the first by . Then the number of terms in the series is ______.