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A particular form of electromagnetic radiation has a frequency of $8.11 \times 10^{14} \mathrm{Hz}$. (a) What is its wavelength in nanometers? In meters? (b) To what region of the electromagnetic spectrum would you assign it? (c) What is the energy (in joules) of one quantum of this radiation?

A) $3.70 \times 10^{-7} \mathrm{m}=3.70 \times 10^{2} \mathrm{nm}$B) Ultraviolet region $\mathrm{C}) \mathrm{E}=5.37 \times 10^{-19} \mathrm{J}$

Chemistry 101

Chapter 7

Quantum Theory and the Electronic Structure of Atoms

Electronic Structure

Carleton College

University of Kentucky

Brown University

Lectures

04:49

In chemistry and physics, electronic structure is the way the electrons of an atom are arranged in relationship to the nucleus. It is determined by the subshells the electrons are bound to, which are in turn determined by the principal quantum number ("n") and azimuthal quantum number ("l"). The electrons within an atom are attracted to the protons in the nucleus of that atom. The number of electrons bound to the nucleus is equal to the number of protons in the nucleus, which is called the atomic number ("Z"). The electrons are attracted to the nucleus by this mutual attraction and are bound to the nucleus. The electrons within an atom are attracted to each other and this attraction determines the electron configuration. The electron configuration is described by the term symbol, which is the letter used to identify each subshell.

16:45

In physics, the wave–particle duality is the concept that every object or process, no matter how large or how small, behaves as both a wave and a particle. The wave–particle duality is one of the central concepts in quantum mechanics.

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Okay. This question is asking about this question. Asked us to find the wavelength of a a form of electromagnetic radiation of a certain frequency in, uh, meters and animators and how much energy is associated with one quanta or one peace or molecule of this energy. So we can say. And what? Ah, what range this, uh, this electromagnetic radiation is found desks. So we can go ahead and say that since we have the frequency, you know that wavelength is equal to speed of light, which is three times 10 to the eighth, invited by frequency which were given in the problem is being 8.11 times 10 to the 14 hurts. And we know that we're going to get meters because speed of light is given as meters per second and hurts is also equal to inverse seconds. He's gonna cancel out. We're going to get 3.7 times 10 to the negative seventh meters. We can convert this into nanometers because we know that nanometers is times 10 to the negative night. So we could actually move this decimal place over to, and we would get 300 in 70 nana meters, which is equal to 300 or 3.7 times three and seven times in the negative ninth, which we know equals nanometers. So this is the wavelength of the given electromagnetic energy. And this is in the ultraviolet. Ah, the ultraviolet area of the spectrum, which is between 10 nanometers and 400 nanometers. This is just less than the wavelength of the visible spectrum. I also asked, what is the quanta? What is the introduces you with one quanta of this, the energy of this frequency. So we know that that is equal to energy equals plank's constant times. Frequency price constant is 6.63 times 10 to the negative. 34 Jules per second and we're multiplying by the frequency. So we know that the second's gonna cancel out and leave us with jewels, which is what we're looking for, considering we're looking for energy. Jewels is the unit of energy, where the frequency would be 8.11 times 10 to the for tink hurts. This will be played in the calculator is gonna come out to be 5.37 times 10 through the negative 19th. Jules for one specific quanta of the electromagnet creation. Shut up. So just to recap, we found the wavelength to be 307 Anna Meares and 3.7 times seven, the native seventh nanometers. We know that that is in the UV range of the electromagnetic spectrum. Between 10 and 400 animators re plugged it into the equation to find energy. So we multiply the frequency transplants constant to get 35.37 times sends the negative 19th jewels.

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