The first three energy levels of the fictitious element Xare shown in (Figure 1)

Question

The first three energy levels of the fictitious element Xare shown in (Figure 1) .

https://session.masteringphysics.com/problemAsset/1820162/8/jfk.Figure.29.P52.jpg

Part A

What wavelengths are observed in the absorption spectrum of element X?

Enter your answers in descending order separated by commas.

Part C

An electron with a speed of 2.3 ×106m/scollides with an atom of element X. Shortly afterward, the atom emits a 1240 nmphoton. 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.

Express your answer with the appropriate units.

Explanation / Answer

from the diagram following are the energy levels

E1 = -6.5 eV

E2 = -3 eV

E3 = -2 eV

A. in absorption spectrum, following energies are absorbed

E3 - E1, E3 - E2, E2 - E1

4.5 eV, 1 eV, 3.5 eV

now, E = hc/lambda*e ( e is charge of electron)

E = 0.000001243125/lambda

hence

lambda1 = 276.25 nm

lambda2 = 1243.125 nm

lambda3 = 355.178 nm

C. v = 2.3*10^6 m/s

energy gained by atom = energy of 1240 nm photon = 1 eV

hence

final speed of electron = u

0.5*9.1*10^-31*v^2 = 1.6*10^-19 + 0.5*9.1*10^-31*u^2

u = 2.2222*10^6 m/s

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