Calculating Fraction of Kinetic Energy Transferred in Head-on Collision

AI Thread Summary
The discussion focuses on calculating the fraction of kinetic energy transferred from an electron to a mercury atom during a head-on elastic collision. The key equations involve the conservation of kinetic energy and momentum, with the fraction of kinetic energy expressed as Kf/Ki, where Kf is the final kinetic energy and Ki is the initial kinetic energy. Participants discuss deriving the final velocity of the electron (v2) in terms of its initial velocity (v1) using momentum concepts. However, there is a challenge in obtaining a numerical value for the fraction of kinetic energy transferred. The conversation highlights the need for further assistance in resolving the calculation.
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Determine from classical mechanics (using a head-on collision with recoil at 180 degrees) what fraction of an electron’s kinetic energy can be transferred to a mercury atom in an elastic collision. Derive an approximate value of the fraction.

well ok let the mass of the electron be m_e
initial velocity of electron v_1
fina lvelocity v_2
mercury atom mass m_Hg
mercury atom fina lvelocity v_Hg

\frac{1}{2} m_{e} v_{1}^2 = \frac{1}{2} m_{Hg} v_{Hg}^2 + \frac{1}{2} m_{e} v_{2}^2

the fraction of kinetic energy is Kf/Ki right

\frac{K_{f}}{K_{i}} = \frac{v_{2}^2}{v_{1}^2}

do i use momentum concepts to find v2 in terms of v1

still it doesn't give me a numerical value... if that's what the question is asking...
 
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