Question

An electron and photon have same wavelength. If $E$ is the energy of photon and $p$ is the momentum of electron, then the magnitude of $\frac{E}{p}$ in SI unit is (a) $3.33 \times 10^{-9}$ (b) $3.0 \times 10^{8}$ (c) $1.1 \times 10^{-19}$ (d) $9 \times 10^{16}$

Name: Problem 47, Chapter 25: Master Resource Book in JEE Main Physics
Uploaded: 2022-01-23T07:10:59-08:00
Duration: 1 min 48 s
Channel: Yuva S
Description: An electron and photon have same wavelength. If E is the energy of photon and p is the momentum of electron, then the magnitude of (E)/(p) in SI unit is (a) 3.33 ×10^-9 (b) 3.0 ×10^8 (c) 1.1 ×10^-19 (d) 9 ×10^16

    An electron and photon have same wavelength. If $E$ is the energy of photon and $p$ is the momentum of electron, then the magnitude of $\frac{E}{p}$ in SI unit is
(a) $3.33 \times 10^{-9}$
(b) $3.0 \times 10^{8}$
(c) $1.1 \times 10^{-19}$
(d) $9 \times 10^{16}$

Master Resource Book in JEE Main Physics

D. B. Singh 1st Edition

Chapter 25, Problem 47

Instant Answer

Solved by Expert Yuva S

01/23/2022

Step 1

Step 1: We know that the momentum of an electron is given by the formula $p = \frac{h}{\lambda}$, where $h$ is Planck's constant and $\lambda$ is the wavelength. Show more…

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An electron and photon have same wavelength. If $E$ is the energy of photon and $p$ is the momentum of electron, then the magnitude of $\frac{E}{p}$ in SI unit is (a) $3.33 \times 10^{-9}$ (b) $3.0 \times 10^{8}$ (c) $1.1 \times 10^{-19}$ (d) $9 \times 10^{16}$

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Key Concepts

De Broglie Momentum

According to the de Broglie hypothesis, every particle has wave-like properties and its wavelength is given by ? = h/p, where p is the momentum of the particle. This relation applies to electrons and other matter particles, establishing a fundamental connection between momentum and wavelength.

Ratio of Energy to Momentum

When comparing the energy of a photon and the momentum of an electron that share the same wavelength, the expressions E = hc/? and p = h/? lead to the ratio E/p equaling c, since the factors h and ? cancel out. This highlights the intrinsic link between these quantities and the universal constant, the speed of light.

Photon Energy

The energy of a photon is given by the equation E = hc/?, where h is Planck's constant, c is the speed of light, and ? is the wavelength. This relation shows that a photon's energy is inversely proportional to its wavelength.

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