An electron moving with a speed of 6.3 times 10^6 m/s collides with a lithium io

Question

An electron moving with a speed of 6.3 times 10^6 m/s collides with a lithium ion (Li^++) in its ground state, which then emits a photon. What is the smallest possible wavelength of the emitted photon? (You may assume the speed of the lithium ion is negligible at all times.) Challenge A: How many total possibilities are there for the wavelength of the emitted photon? Challenge B: What is the largest possible wavelength of the emitted photon? Challenge C: What is the electron's speed after the collision?

Explanation / Answer

Initial energy of electron E= 0.5mv^2 = 0.5*9.1e-31*6.3e6^2

= 1.806*10^-17 J

Smallest wavelength = hc/E

= 6.626e-34*3e8/1.806e-17

= 11*10^-9 m

= 11 nm

Largest wavelength is infinity

Infinite number of possibilities are there.

For minimum wavelength of photon, electron speed is zero.

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