Quickly, can someone please solve this problem? I\'d greatly appreciate it. The

Question

Quickly, can someone please solve this problem? I'd greatly appreciate it.

The first three energy levels of the fictitious element X are shown in (Figure 1) An electron with a speed of 1.6 times 10^6 m/s collides with an atom of element X. Shortly afterward, the atom emits a 1240 nm photon. What was the electron's speed after the collision? Assume that, because the atom is so much more massive than the electron, the recoil of the atom is negligible. Express your answer with the appropriate units.

Explanation / Answer

Since subatomic particles undergo perfectly elastic collision, we can use the conservation of energy,

mv^2/2= hc/ (lambda) + mV ^2/2

Here, hc/ (lamda) = 1 ev = 1.6 x 10^-19 J

V= sqrt(v^2 + 1.6 x 10^-19 x 2/m)

sqrt( 2.56 x 10^12 + 3.2 x 10^-19/ 9.1 x 10^-31)

sqrt(2.56 x 10^12 + 0.351 x 10^12) = 10^6 sqrt(2.56+0.351)

= 1.706 x 10^6 m/s approx.

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