Question

An $\alpha$ -particle has initial kinetic energy of 25 eV and it is accelerated through the potential difference of 150 volt. If a proton has initial kinetic energy of 25 eV and it is accelerated through the potential difference of 25 volt then find the approximate ratio of the final wavelengths associated with the proton and the $\alpha$ particle.

• A. 5:1
• B. 13:5
• C. 26:1
  
• D. 26:5
  

Answer 1

The correct option is C 26:1

For α -particle, total kinetic energy $=25+2\times 150=25+300=325eV$
For proton, total kinetic energy $=25+1\times 25=50eV$
$\frac{{\lambda }_{\alpha }}{{\lambda }_p}=\frac{m_{p}K.E_p}{m_{\alpha }K.E_{\alpha }}$
$=\frac{1\times 50}{4\times 325}=\frac{50}{1300}=1:26$
Hence, the approximate ratio of the final wavelengths associated with the proton and the α particle is 26 :1.