Answer:
Explanation:
1. Formulae:
Where:
2. Reasoning
An alha particle contains 2 neutrons and 2 protons, thus its mass number is 4.
A proton has mass number 1.
Thus, the relative masses of an alpha particle and a proton are:
[tex]\dfrac{m_\alpha}{m_p}=4[/tex]
For the kinetic energies you find:
[tex]\dfrac{E_\alpha}{E_p}=\dfrac{m_\alpha \times v_\alpha^2}{m_p\times v_p^2}[/tex]
[tex]\dfrac{1eV}{4eV}=\dfrac{4\times v_\alpha^2}{1\times v_p^2}\\\\\\\dfrac{v_p^2}{v_\alpha^2}=16\\\\\\\dfrac{v_p}{v_\alpha}=4[/tex]
Thus:
[tex]\dfrac{m_\alpha}{m_p}=4=\dfrac{v_p}{v__\alpha}[/tex]
[tex]m_\alpha v_\alpha=m_pv_p[/tex]
From de-Broglie equation, λ = h/(mv)
[tex]\dfrac{\lambda_p}{\lambda_\alpha}=\dfrac{m_\lambda v_\lambda}{m_pv_p}=\dfrac{1}{1}=1:1[/tex]
