The ratio of wavelengths of proton and deuteron accelerated by potential $V_p$ and $V_d$ is $1: \sqrt{2}$ Then, the ratio of $V_p$ to $V_d$ will be
- $1: 1$
- $\sqrt{2}: 1$
- $2: 1$
- $4: 1$
The Correct Option is D
Solution and Explanation
The correct option is (D) : 4:1
The kinetic energy gained by a charged particle accelerated by a potential V is qV
KE=qV
⇒2mp2=qV⇒p=\(\sqrt{2mqV}\)
p=λh, thus λ=\(\frac{h}{\sqrt{2mqV}}\)
now \(\frac{\lambda_p}{\lambda_d}\)=\(\sqrt{\frac{m_dV_d}{M_pV_p}}\)
\(\Rightarrow\)\(\frac{1}{\sqrt2}\)=\(\sqrt{\frac{2V_d}{V_p}}\)\(\Rightarrow\)\(\frac{V_p}{V_d}\)=4
Top Questions on Dual nature of radiation and matter
- A light wave described by E = 60[\(\sin(3 \times 10^{15})t + \sin(12 \times 10^{15})t\)] (in SI units) falls on a metal surface of work function 2.8 eV. The maximum kinetic energy of ejected photoelectron is (approximately)________ eV. (h=\(6.6 \times 10^{-34}\) J.s. and e=\(1.6 \times 10^{-19}\) C)
- JEE Main - 2026
- Physics
- Dual nature of radiation and matter
- Find the ratio of de-Broglie wavelengths of deuteron having energy E and \(\alpha\)-particle having energy 2E :
- CUET (UG) - 2026
- Physics
- Dual nature of radiation and matter
- Whether the total mass of nuclei increases, decreases or remains unchanged?
- CBSE CLASS XII - 2025
- Physics
- Dual nature of radiation and matter
- A laser beam of frequency \( 3.0 \times 10^{14} \) Hz produces average power of 9 mW. Find (i) the energy of a photon of the beam, and (ii) the number of photons emitted per second on an average by the source.
- CBSE CLASS XII - 2025
- Physics
- Dual nature of radiation and matter
- The momentum (in kg·m/s) of a photon of frequency \( 6.0 \times 10^{14} \) Hz is:
- CBSE CLASS XII - 2025
- Physics
- Dual nature of radiation and matter
Questions Asked in JEE Main exam
In the following \(p\text{–}V\) diagram, the equation of state along the curved path is given by \[ (V-2)^2 = 4ap, \] where \(a\) is a constant. The total work done in the closed path is:
- JEE Main - 2026
- Thermodynamics
Let \( ABC \) be a triangle. Consider four points \( p_1, p_2, p_3, p_4 \) on the side \( AB \), five points \( p_5, p_6, p_7, p_8, p_9 \) on the side \( BC \), and four points \( p_{10}, p_{11}, p_{12}, p_{13} \) on the side \( AC \). None of these points is a vertex of the triangle \( ABC \). Then the total number of pentagons that can be formed by taking all the vertices from the points \( p_1, p_2, \ldots, p_{13} \) is ___________.
- JEE Main - 2026
- Coordinate Geometry
- A voltage regulating circuit consisting of a Zener diode having breakdown voltage of $10\,\text{V}$ and maximum power dissipation of $0.4\,\text{W}$ is operated at $15\,\text{V}$. The approximate value of protective resistance in this circuit is ___ $\Omega$.
- JEE Main - 2026
- Semiconductor electronics: materials, devices and simple circuits
- Two point charges of \(1\,\text{nC}\) and \(2\,\text{nC}\) are placed at two corners of an equilateral triangle of side \(3\) cm. The work done in bringing a charge of \(3\,\text{nC}\) from infinity to the third corner of the triangle is ________ \(\mu\text{J}\). \[ \left(\frac{1}{4\pi\varepsilon_0}=9\times10^9\,\text{N m}^2\text{C}^{-2}\right) \]
- JEE Main - 2026
- Electrostatics
Consider the following two reactions A and B:
The numerical value of [molar mass of $x$ + molar mass of $y$] is ___.
- JEE Main - 2026
- Organic Chemistry