KCET · Physics · Dual Nature of Matter
An electron of mass \(m_{e}\) and a proton of mass \(m_{p}\) are moving with the same speed. The ratio of their de-Broglie's wavelengths \(\lambda_{e} / \lambda_{p}\) is
- A 1
- B 1836
- C \(\frac{1}{1836}\)
- D 918
Answer & Solution
Correct Answer
(B) 1836
Step-by-step Solution
Detailed explanation
de-Broglie's wavelength,
\[
\lambda=\frac{h}{m v}
\]
For electron,
\[
\lambda_{e}=\frac{h}{m_{e} v}
\]
For photon,
\[
\lambda_{p}=\frac{h}{m_{p} v}
\]
\(\begin{aligned} \frac{\lambda_{e}}{\lambda_{p}} &=\frac{h / m_{e} v}{h / m_{p} v} \\ \frac{\lambda_{e}}{\lambda_{p}} &=\frac{m_{p}}{m_{e}} \\ \frac{\lambda_{e}}{\lambda_{p}}=\frac{1.67 \times 10^{-27}}{9.1 \times 10^{-31}} &=0.18 \times 10^{4}=1836 \end{aligned}\)
\[
\lambda=\frac{h}{m v}
\]
For electron,
\[
\lambda_{e}=\frac{h}{m_{e} v}
\]
For photon,
\[
\lambda_{p}=\frac{h}{m_{p} v}
\]
\(\begin{aligned} \frac{\lambda_{e}}{\lambda_{p}} &=\frac{h / m_{e} v}{h / m_{p} v} \\ \frac{\lambda_{e}}{\lambda_{p}} &=\frac{m_{p}}{m_{e}} \\ \frac{\lambda_{e}}{\lambda_{p}}=\frac{1.67 \times 10^{-27}}{9.1 \times 10^{-31}} &=0.18 \times 10^{4}=1836 \end{aligned}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- Two heating coils of resistances \( 10 \Omega \) and \( 20 \Omega \) are connected in parallel and connected to a battery of emf \( 12 \mathrm{~V} \) and internal resistance \( 1 \Omega \). The power consumed by them are in the ratioKCET 2016 Easy
- For a point object, which of the following always produces virtual image in air?KCET 2023 Easy
- A \(1 \mathrm{~kg}\) ball moving at \(12 \mathrm{~ms}^{-1}\) collides with a \(2 \mathrm{~kg}\) ball moving in opposite direction at \(24 \mathrm{~ms}^{-1}\). If the coefficient of restitution is \(2 / 3\), then their velocities after the collision areKCET 2021 Hard
- If the radius of first Bohr orbit is \(r\), then the radius of the second Bohr orbit will beKCET 2025 Easy
- In Raman effect, Stokes' lines are spectral lines havingKCET 2007 Medium
- Consider an electrical conductor connected across a potential difference \(V\). Let \(\Delta q\) be a small charge moving through it in time \(\Delta t\). If \(I\) is the electric current through it,
I. the kinetic energy of the charge increases by \(I V \Delta t\).
II. the electric potential energy of the charge decreases by \(I V \Delta t\).
III. the thermal energy of the conductor increases by IV \(\Delta t\).
Choose the correct option.KCET 2021 Easy
More PYQs from KCET
- In the circuit shown, the end \(A\) is at potential \(V_0\) and end \(B\) is grounded. The electric current \(I\) indicated in the circuit is
KCET 2024 Medium - Which of the following has the lowest boiling point?KCET 2020 Medium
- Match List-I and List-II with respect to proteins and their functions and select the correct option.
List-I List-II 1. Collagen p. Fights infectious agents 2. Trypsin q. Hormone 3. Insulin r. Enzyme 4. Antibody s. Intercellular ground substance KCET 2023 Hard - The edible part of the fruit of apple isKCET 2016 Medium
- The gene disorder phenylketonuria is an example forKCET 2016 Hard
- When an electrolyte is dissociated in solution, the van't Hoff's factor (i) is,KCET 2016 Easy