An electron with speed υ and a photon with speed c have the same de-Broglie wavelength. If the kinetic energy and momentum of electron are Ee and pe and that of photon are Eph and pph respectively. Which of the following is correct?
\(\frac{E_e}{E_{\text{ph}}} = \frac{2c}{v}\)
\(\frac{E_e}{E_{\text{ph}}} = \frac{v}{2c}\)
\(\frac{p_e}{p_{\text{ph}}} = \frac{2c}{v}\)
\(\frac{p_e}{p_{\text{ph}}} = \frac{v}{2c}\)
The Correct Option is B
Solution and Explanation
\(\lambda_e = \lambda_{\text{ph}}\)
\(⇒\) \(\frac{h}{p_e} = \frac{hc}{E_{\text{ph}}}\)
\(⇒\) \(E_{\text{ph}} = p_e \cdot c = 2E_e \left(\frac{c}{v}\right)\)
\(⇒\) \(\frac{E_e}{E_{\text{ph}}} = \frac{v}{2c}\)
So, Option (B)
Top Questions on de broglie hypothesis
- If we consider an electron and a photon with the same de-Broglie wavelength, then they will have the same
- KCET - 2025
- Physics
- de broglie hypothesis
- A photon and an electron have the same energy \( E \). If \( \lambda_p \) is the wavelength of the photon and \( \lambda_e \) is the de Broglie wavelength of the electron, then the ratio \( \frac{\lambda_p}{\lambda_e} \) is:
- MHT CET - 2025
- Physics
- de broglie hypothesis
- A photon and an electron have the same energy \( E \). If \( \lambda_p \) is the wavelength of the photon and \( \lambda_e \) is the de Broglie wavelength of the electron, then the ratio \( \frac{\lambda_p}{\lambda_e} \) is:
- MHT CET - 2025
- Physics
- de broglie hypothesis
If \( \lambda \) and \( K \) are de Broglie wavelength and kinetic energy, respectively, of a particle with constant mass. The correct graphical representation for the particle will be:
- JEE Main - 2025
- Physics
- de broglie hypothesis
The wavelength of an electron is \( 10^3 \) nm. What is its momentum in kg m s\(^{-1}\)?
- TS EAMCET - 2024
- Chemistry
- de broglie hypothesis
Questions Asked in JEE Main exam
The remainder when \( 64^{64} \) is divided by 7 is equal to:
- JEE Main - 2025
- Arithmetic Progression
- The sum of the infinite series $ \cot^{-1} \left( \frac{7}{4} \right) + \cot^{-1} \left( \frac{19}{4} \right) + \cot^{-1} \left( \frac{39}{4} \right) + \cot^{-1} \left( \frac{67}{4} \right) + ... $ is:
- JEE Main - 2025
- Sequence and series
- If $ \alpha $ is a root of the equation $ x^2 + x + 1 = 0 $ and $$ \sum_{k=1}^{n} \left( \alpha^k + \frac{1}{\alpha^k} \right)^2 = 20$$, then n is equal to _______
- JEE Main - 2025
- Sequence and series
x mg of Mg(OH)$_2$ (molar mass = 58) is required to be dissolved in 1.0 L of water to produce a pH of 10.0 at 298 K. The value of x is ____ mg. (Nearest integer) (Given: Mg(OH)$_2$ is assumed to dissociate completely in H$_2$O)
- JEE Main - 2025
- Equilibrium
- The amount of calcium oxide produced on heating 150 kg limestone (75% pure) is _______ kg. (Nearest integer)
Given: Molar mass (in g mol$^{-1}$) of Ca-40, O-16, C-12- JEE Main - 2025
- Stoichiometry and Stoichiometric Calculations
Concepts Used:
Electron Transport System
The electron transport chain or system is the sequence of electron carriers, enzymes, and cytochrome that passes electrons from one to another through the redox reaction. It is electron transport-linked phosphorylation.
It contains flavin nucleotides (FAD), nicotinamide adenine dinucleotide (NAD), coenzyme Q, and cytochromes localized in F1 particles of mitochondria. It occurs in the inner mitochondrial membrane along with cristae.
In this process five (5) complexes are involved namely, I- NADH-UQ reductase, II- Succinate-UQ reductase, III- UQH2 -cytochrome C reductase, IV- Cytochrome C oxidase, and V is connected with F0−F1 particles.
In this process, NAD and FAD are minimized.
Steps:
- Redox at complex I: Four (4) protons are pumped from the matrix to intermembrane space.
- Redox at complex II: Coenzyme Q collects the electrons from complex I and II, and goes to complex III.
- Redox of complex III: Four (4) protons are again pumped from matrix to intermembrane space and cytochrome C transports electrons to the complex IV.
- Redox of complex IV: Two (2) protons are pumped from the matrix to intermembrane space and the formation of water occurs in the matrix.
- ATP synthase action: It pumps protons from intermembrane space to matrix and generates ATP. It is associated with oxidative phosphorylation.