The wavelength of a very fast-moving electron | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) According to the de Broglie hypothesis,the wavelength $\lambda$ is given by $\lambda = \frac{h}{p}$,where $p$ is the momentum of the particle.For

Vedclass · Accepted Answer

$\lambda = \frac{h}{m_0 v / \sqrt{1 - \frac{v^2}{c^2}}}$

Vedclass · Answer

(A) According to the de Broglie hypothesis,the wavelength $\lambda$ is given by $\lambda = \frac{h}{p}$,where $p$ is the momentum of the particle.For a particle moving at relativistic speeds $(v \approx c)$,the mass $m$ is given by the relativistic mass formula: $m = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}}$,where $m_0$ is the rest mass.The momentum $p$ is defined as $p = m \cdot v$.Substituting the expression for relativistic mass into the momentum formula,we get: $p = \frac{m_0 v}{\sqrt{1 - \frac{v^2}{c^2}}}$.Finally,substituting this into the de Broglie wavelength equation,we obtain: $\lambda = \frac{h}{m_0 v / \sqrt{1 - \frac{v^2}{c^2}}}$.

The wavelength of a very fast-moving electron $(v \approx c)$ is:

Similar Questions

The de-Broglie wavelength of an electron having $80 \ eV$ of energy is nearly .............. $\mathring{A}$ ($1 \ eV = 1.6 \times 10^{-19} \ J$,Mass of electron $= 9 \times 10^{-31} \ kg$,Planck's constant $= 6.6 \times 10^{-34} \ J \cdot s$).

What is the de Broglie wavelength of a nitrogen molecule in air at $300 \;K$ (in $nm$)? Assume that the molecule is moving with the root-mean-square speed of molecules at this temperature. (Atomic mass of nitrogen $= 14.0076 \;u$)

The de Broglie wavelength of a proton accelerated by a potential difference of $100 \ V$ is $\lambda_0$. If an alpha particle is accelerated by the same potential difference,its de Broglie wavelength will be:

In an optical microscope, which electromagnetic waves are used? Which type of waves are used in an electron microscope?

The magnitude of the de-Broglie wavelength $(\lambda)$ of electron $(e)$,proton $(p)$,neutron $(n)$ and $\alpha-$ particle $(\alpha)$ all having the same energy of $1\,MeV$,in the increasing order will follow the sequence

Vedclass Test Series

Exam Paper Generator

Online Exam Module