An electron with a speed of 1.5×106m/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. Hint: The energy of the photon is not the energy transferred to the atom in the collision.

The speed of electron after the collision is .

Given data:

The speed of electron before collision is, .

The wavelength of photon is, .

Let v is the electron's speed after the collision. The according to conservation of energy concept, "the total energy of the electron remains conserved". Hence, the loss of energy of electron is equal energy of the emitted photon such that :

Energy loss of electron = Energy emitted by photon

Here, h is the Planck's constant, m is the mass of electron and c is the speed of light.

Solving as,

Thus, the speed of electron after the collision is .

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The electron's speed after the collision is .

Explanation:

We have,

Initial speed of an electron,

Wavelength of a photon,

Let v is the electron's speed after the collision. The total energy of the electron remains conserved in this case. The loss of energy of electron is equal energy of the emitted photon such that :

m is mass of electron

Putting all the values,

So, the electron's speed after the collision is .

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