The de Broglie wavelengths for an electron and a photon are λe and λp, respectively. For the same kinetic energy of electron and photon, which of the following presents the correct relation between the de Broglie wavelengths of two?
\(λ_p ∝ λ^{2}_e\)
\(λ_p ∝ λ_e\)
\(λ_p ∝ \sqrtλ_e\)
\(λ_p ∝ \sqrt{\frac{1}{λ_e}}\)
The Correct Option is A
Solution and Explanation
The correct answer is (A) : \(λ_p ∝ λ^{2}_e\)
\(λ_p = \frac{h}{p} = \frac{hc}{E} .... (i)\)
\(λ_e = \frac{h}{\sqrt{2mE}} .... (ii)\)
From (i) and (ii)
\(λ_p ∝ λ^{2}_e\)
Top Questions on Dual nature of matter
- Choose the correct statement:
- CBSE CLASS XII - 2025
- Physics
- Dual nature of matter
- An ideal gas mixture of C\(_2\)H\(_6\) and C\(_2\)H\(_4\) occupies a volume of 28 L at 1 atm and 273 K. This mixture reacts completely with 128 g of O\(_2\) to produce CO\(_2\) and H\(_2\)O(\(l\)). What is the mole fraction of C\(_2\)H\(_4\) in the mixture ?
- AP EAPCET - 2025
- Chemistry
- Dual nature of matter
- Choose the incorrect statement from the following
- AP EAPCET - 2025
- Chemistry
- Dual nature of matter
- If the de Broglie wavelength of an electron is \( 2 \, \text{nm} \), then its kinetic energy is nearly (Planck's constant \( = 6.6 \times 10^{-34} \, \text{J s} \) and mass of electron \( = 9 \times 10^{-31} \, \text{kg} \))
- AP EAPCET - 2025
- Physics
- Dual nature of matter
An alpha particle moves along a circular path of radius 0.5 mm in a magnetic field of \( 2 \times 10^{-2} \, \text{T} \). The de Broglie wavelength associated with the alpha particle is nearly
(Planck’s constant \( h = 6.63 \times 10^{-34} \, \text{Js} \))- AP EAPCET - 2025
- Physics
- Dual nature of matter
Questions Asked in JEE Main exam
- If the equation of the parabola with vertex $\left(\frac{3}{2},\, 3\right)$ and the directrix $x + 2y = 0$ is
$$ ax^2 + by^2 - cxy - 30x - 60y + 225 = 0, $$ then $\alpha + \beta + \gamma$ is equal to:- JEE Main - 2025
- Calculus
- In a first order decomposition reaction, the time taken for the decomposition of reactant to one fourth and one eighth of its initial concentration are $ t_1 $ and $ t_2 $ (s), respectively. The ratio $ t_1 / t_2 $ will be:
- JEE Main - 2025
- Chemical Kinetics
- HA $ (aq) \rightleftharpoons H^+ (aq) + A^- (aq) $ The freezing point depression of a 0.1 m aqueous solution of a monobasic weak acid HA is 0.20 °C. The dissociation constant for the acid is Given: $ K_f(H_2O) = 1.8 \, \text{K kg mol}^{-1} $, molality ≡ molarity
- JEE Main - 2025
- Colligative Properties
20 mL of sodium iodide solution gave 4.74 g silver iodide when treated with excess of silver nitrate solution. The molarity of the sodium iodide solution is _____ M. (Nearest Integer value) (Given : Na = 23, I = 127, Ag = 108, N = 14, O = 16 g mol$^{-1}$)
- JEE Main - 2025
- Stoichiometry and Stoichiometric Calculations
- Which of the following binary mixture does not show the behavior of minimum boiling azeotropes?
- JEE Main - 2025
- Solutions
Concepts Used:
Dual Nature of Radiation and Matter
The dual nature of matter and the dual nature of radiation were throughgoing concepts of physics. At the beginning of the 20th century, scientists untangled one of the best-kept secrets of nature – the wave-particle duplexity or the dual nature of matter and radiation.
Electronic Emission
The least energy that is needed to emit an electron from the surface of a metal can be supplied to the loose electrons.
Photoelectric Effect
The photoelectric effect is a phenomenon that involves electrons getting away from the surface of materials.
Heisenberg’s Uncertainty Principle
Heisenberg’s Uncertainty Principle states that both the momentum and position of a particle cannot be determined simultaneously.