An electron having de-Broglie wavelength lamb | vedclass

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

Question

(C) Let $K$ be the kinetic energy of the electron.The de-Broglie wavelength of the electron is given by $\lambda = \frac{h}{p} = \frac{h}{\sqrt{2mK}}$

Vedclass · Accepted Answer

$\lambda_0 = \frac{2mc\lambda^2}{h}$

Vedclass · Answer

(C) Let $K$ be the kinetic energy of the electron.The de-Broglie wavelength of the electron is given by $\lambda = \frac{h}{p} = \frac{h}{\sqrt{2mK}}$.Squaring both sides,we get $\lambda^2 = \frac{h^2}{2mK}$,which implies $K = \frac{h^2}{2m\lambda^2}$.The cut-off wavelength $\lambda_0$ for continuous $X$-rays is determined by the maximum energy of the photon,which equals the kinetic energy of the incident electron: $E = \frac{hc}{\lambda_0} = K$.Substituting the value of $K$,we get $\frac{hc}{\lambda_0} = \frac{h^2}{2m\lambda^2}$.Solving for $\lambda_0$,we find $\lambda_0 = \frac{hc \cdot 2m\lambda^2}{h^2} = \frac{2mc\lambda^2}{h}$.Therefore,option $(C)$ is correct.

An electron having de-Broglie wavelength $\lambda$ is incident on a target in an $X$-ray tube. The cut-off wavelength of the emitted $X$-ray is:

Similar Questions

Atomic number of anticathode material in an $X$-ray tube is $41$. Wavelength of $K_\alpha$ $X$-ray produced in the tube is ........ $\mathring A$.

If the operating voltage of an $X$-ray tube is $50 \, kV$,then the velocity of the $X$-rays is . . . . .

If the energy of an electron in the $K$-shell is $40000 \,eV$ and an accelerating potential of $60000 \,eV$ is applied across a Coolidge tube,which of the following $X$-rays will be obtained?

$X$-rays will travel the minimum distance in which of the following materials?

The range of wavelength for $X$-rays is from . . . . . . .

Vedclass Test Series

Exam Paper Generator

Online Exam Module