The first three energy levels of the E(e v) fictitious...

The first three energy levels of the $E(e v)$ fictitious element $X$ are shown in 0.00 a. What is the ionization energy of element $\mathbf{X} ?$ b. What wavelengths are observed in the absorption spectrum of element X? Express your answers in $\mathrm{nm}$. (FIGURE CAN'T COPY) c. State whether each of your wavelengths in part b corresponds to ultraviolet, visible, or infrared light. d. An electron with a speed of $1.4 \times 10^{6} \mathrm{m} / \mathrm{s}$ collides with an atom of element X. Shortly afterward, the atom emits a $1240 \mathrm{nm}$ 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. (FIGURE CAN'T COPY)

The first three energy levels of the
$E(e v)$
fictitious element $X$ are shown in
0.00
a. What is the ionization energy of element $\mathbf{X} ?$
b. What wavelengths are observed in the absorption spectrum of element
X? Express your answers in $\mathrm{nm}$.
(FIGURE CAN'T COPY)
c. State whether each of your wavelengths in part b corresponds to ultraviolet, visible, or infrared light.
d. An electron with a speed of $1.4 \times 10^{6} \mathrm{m} / \mathrm{s}$ collides with an atom of element X. Shortly afterward, the atom emits a $1240 \mathrm{nm}$ 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.
(FIGURE CAN'T COPY)

Key Concepts

Electromagnetic Spectrum Regions

The electromagnetic spectrum is divided into regions such as ultraviolet, visible, and infrared light, each defined by a specific range of wavelengths. Assigning calculated wavelengths to these categories helps in understanding the nature of the observed radiation and is critical in spectroscopic analysis.

Ionization Energy

Ionization energy is the energy required to remove an electron completely from an atom, typically from the ground state to a state where the electron is free. It represents the energy difference between the bound state and the continuum and is a fundamental property that determines how an element interacts chemically and physically.

Energy Level Transitions

Energy level transitions refer to the process where an electron moves between discrete energy states within an atom. When an electron absorbs energy, it is excited from a lower to a higher energy level, and when it emits energy (often as a photon), it falls back to a lower level. The precise energy difference between levels dictates the energy (and thus the wavelength) of the absorbed or emitted light.

Photon Energy and Wavelength Calculation

The relationship between the energy of a photon and its wavelength is governed by the equation E = hc/?, where h is Planck's constant and c is the speed of light. This concept is vital for converting the energy differences between electronic states into specific wavelengths, which in turn helps in analyzing the absorption or emission spectrum of an element.

Conservation of Energy in Electron-Atom Collisions

In collisions between electrons and atoms, conservation of energy dictates that the total energy before and after the collision remains constant. When an electron collides with an atom, part of its kinetic energy can be transferred to the atom, which may lead to changes in the electron's speed and the promotion of the atom's electrons to higher energy levels. The energy not retained by the electron is manifested in the excitation and subsequent photon emission from the atom.

Transcript

00:01 For the first part of this question, we are looking at finding what is the ionization energy.

00:06 Now we are given the three lowest energy states for atom.

00:13 And the thing we want to take down off is that the energy levels are given in negative values.

00:18 So what this means is that it is with reference to the ionization level.

00:30 And so the ionization energy in this case would be 0 ev.

00:36 At the top, very very top, would be 0 ev.

00:41 And so the energy required to ionize an electron, ionize the atom from the ground state all the way to 0ev.

00:50 So the energy of ironization would just be taking 0 minus the energy for a ground state, which is negative 6 .5 ev.

01:04 And we will get 6 .5.

01:06 Next we are looking at the absorption spectrum.

01:14 Now the absorption spectrum for these three energy levels that is possible between from 1 to 2 and from 1 to 3.

01:23 Absorption spectrum only starts off with the atom in the ground state.

01:30 Now what we have to find is just the energy of the photons that are being emitted from this transition and from that we can infer one what is the wavelength from the equation e equals to h c over lambda and so lambda must be equals to h c over e where e is the energy difference between the states right during the transition for the transition from 1 to 2 the energy difference is actually minus from minus 3 plus 6 .5 so that is actually 3 .5 now take note that we have to convert ev into joules by multiplying by the conversion factor and we should get our lambda in terms of meters or 355 nanometers.

02:42 We do the same for the other transition that is from 1 to 3 but the energy difference in this case would just be 4 .5 ev and from this we should get the wavelengths to 76 nanometers.

03:01 Now since both of these are wavelengths that are lower than 400 nanometers, right, and we know 400 nanometers is the ultra is near the blue light range, which is the ultraviolet range.

03:17 So these two wavelengths must be ultraviolet.

03:26 Next to, we are considering now that an electron is being bombarded, sorry, it's bombarding the element x, right, the atom.

03:46 It comes in with an initial velocity of 1 .2, sorry, 1 .4, not 1 .2 .4 times 10 power 6 meters per second...

Please give Ace some feedback