A particle has mass m. If its kinetic energy | vedclass

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

Question

(B) The de Broglie wavelength $\lambda$ is given by $\lambda = \frac{h}{p}$,where $p$ is the momentum of the particle.We know that kinetic energy $K$

Vedclass · Accepted Answer

Becomes half

Vedclass · Answer

(B) The de Broglie wavelength $\lambda$ is given by $\lambda = \frac{h}{p}$,where $p$ is the momentum of the particle.We know that kinetic energy $K$ is related to momentum $p$ by the formula $K = \frac{p^2}{2m}$,which implies $p = \sqrt{2mK}$.Substituting this into the wavelength formula,we get $\lambda = \frac{h}{\sqrt{2mK}}$.Let the initial kinetic energy be $K_1$ and the final kinetic energy be $K_2 = 4K_1$.The initial wavelength is $\lambda_1 = \frac{h}{\sqrt{2mK_1}}$ and the final wavelength is $\lambda_2 = \frac{h}{\sqrt{2mK_2}}$.Taking the ratio: $\frac{\lambda_2}{\lambda_1} = \sqrt{\frac{K_1}{K_2}} = \sqrt{\frac{K_1}{4K_1}} = \sqrt{\frac{1}{4}} = \frac{1}{2}$.Therefore,the new de Broglie wavelength $\lambda_2$ becomes half of the initial wavelength $\lambda_1$.

$A$ particle has mass $m$. If its kinetic energy is increased to four times its initial value,what will be the change in its de Broglie wavelength?

Similar Questions

The resolving power of an electron microscope is greater than the resolving power of an optical microscope because

What does the de Broglie equation for an electron represent?

$A$ particle is moving $5$ times as fast as an electron. The ratio of the de-Broglie wavelength of the particle to that of the electron is $1.878 \times 10^{-4}$. The mass of the particle is close to

An electron is accelerated through a potential difference of $10,000 \; V$. Its de Broglie wavelength is,(nearly):
$(m_{e}=9 \times 10^{-31} \; kg)$

What is the ratio of the de Broglie wavelengths of a deuteron and a proton accelerated through the same potential difference?

Vedclass Test Series

Exam Paper Generator

Online Exam Module