Find the ratio of the de Broglie wavelengths | vedclass

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

Question

(A) The de Broglie wavelength $\lambda$ of a particle accelerated through a potential difference $V$ is given by $\lambda = \frac{h}{\sqrt{2mqV}}$.For

Vedclass · Accepted Answer

$2\sqrt{2} : 1$

Vedclass · Answer

(A) The de Broglie wavelength $\lambda$ of a particle accelerated through a potential difference $V$ is given by $\lambda = \frac{h}{\sqrt{2mqV}}$.For a proton $(p)$: $m_p = m$, $q_p = e$.For an $\alpha$-particle $(\alpha)$: $m_{\alpha} = 4m$, $q_{\alpha} = 2e$.The ratio of the wavelengths is:$\frac{\lambda_p}{\lambda_{\alpha}} = \frac{h / \sqrt{2m_p q_p V}}{h / \sqrt{2m_{\alpha} q_{\alpha} V}} = \sqrt{\frac{m_{\alpha} q_{\alpha}}{m_p q_p}}$.Substituting the values:$\frac{\lambda_p}{\lambda_{\alpha}} = \sqrt{\frac{4m 	imes 2e}{m 	imes e}} = \sqrt{8} = 2\sqrt{2}$.Thus, the ratio is $2\sqrt{2} : 1$.

Find the ratio of the de Broglie wavelengths of a proton and an $\alpha$-particle accelerated through the same potential difference.

Similar Questions

An electron of mass $m_{e}$ and a proton of mass $m_{p}$ are accelerated through the same potential difference. The ratio of the de-Broglie wavelength associated with the electron to that with the proton is

Kinetic energy of a proton is equal to energy $E$ of a photon. Let $\lambda_1$ be the de-Broglie wavelength of the proton and $\lambda_2$ be the wavelength of the photon. If $\left(\frac{\lambda_1}{\lambda_2}\right) \propto E^{n}$,then the value of $n$ is:

What is a wave packet?

What is the de Broglie wavelength of an electron accelerated through a potential difference of $ 100 \ V $ (in $\text{Å}$)?

An $\alpha$ particle and a proton are accelerated from rest by a potential difference of $200 \ V$. After this,their de Broglie wavelengths are $\lambda_{\alpha}$ and $\lambda_{p}$ respectively. The ratio $\frac{\lambda_{p}}{\lambda_{\alpha}}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module