Question

In a-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 a-particle.

• A. 5
• B. 4
• C. 3
• D. 2

Answer 1

Answer: (A)

5

Answer 2

$\frac{\lambda_{\rho}}{\lambda\alpha} = \sqrt{\frac{m_{\alpha}KE_{\alpha}}{m_{p}KE_{p}}} = \sqrt{\frac{4m_{p} \times 325}{m_{p} \times 50}} = \sqrt{26} \approx 5.$