1. Tardigrade
  2. Question
  3. Physics
  4. The de-Broglie wavelength associated with an electron and a proton were calculated by accelerating them through same potential of 100 V. What should nearly be the ratio of their wavelengths ? ( m P =1.00727 u , m e =0.00055 u )

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The de-Broglie wavelength associated with an electron and a proton were calculated by accelerating them through same potential of $100\,V$. What should nearly be the ratio of their wavelengths ? $\left( m _{ P }=1.00727\,u ,\,m _{ e }=0.00055\,u \right)$

JEE MainJEE Main 2021Dual Nature of Radiation and Matter

Solution:

$\lambda=\frac{ h }{ mv }=\frac{ h }{\sqrt{2 mK }}=\frac{ h }{\sqrt{2 mqV }}$
$\frac{\lambda_{1}}{\lambda_{2}}=\sqrt{\frac{ m _{2}}{ m _{1}}}$
$\frac{\lambda_{ e }}{\lambda_{ p }}=\sqrt{\frac{ m _{ P }}{ m _{ e }}}=\sqrt{1831.4}=42.79$