Be sure to answer all parts. consider the following energy levels of a hypothetical atom: e4 −2.01 × 10−19 j e3 −5.71 × 10−19 j e2 −1.25 × 10−18 j e1 −1.45 × 10−18 j (a) what is the wavelength of the photon needed to excite an electron from e1 to e4? × 10 m (b) what is the energy (in joules) a photon must have in order to excite an electron from e2 to e3? × 10 j (c) when an electron drops from the e3 level to the e1 level, the atom is said to undergo emission. calculate the wavelength of the photon emitted in this process. × 10 m

(a) 159 nm

First of all, let's calculate the energy difference between the level E1 and E4:

Now we know that this energy difference is related to the wavelength of the absorbed photon by

where

is the Planck constant

is the speed of light

is the wavelength of the photon

Solving for , we find

b) 293 nm

As done in part a), let's calculate the energy difference between the level E2 and E3:

this energy difference is related to the wavelength of the absorbed photon by

Solving for again, we find

c) 226 nm

As done in part a) and b), let's calculate the energy difference between the level E1 and E3:

this energy difference is related to the wavelength of the emitted photon by

Solving for again, we find