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Calculate the frequency (Hz) and wavelength (nm) of the emitted photon when an electron drops from the $n=4$ to the $n=2$ level in a hydrogen atom.

To calculate wavelength we use the following formula:$\lambda=\frac{c}{\nu}$Where, $\boldsymbol{c}=$ speed of light $\approx 3 \cdot 10^{8} \frac{m}{s}$$\boldsymbol{\lambda}=\frac{3 \cdot 10^{8} \frac{m}{s}}{6.17 \cdot 10^{14} \mathrm{H} z} \approx 4.86 \cdot 10^{-7} \mathrm{m}=486 \mathrm{mm}$

Chemistry 101

Chapter 7

Quantum Theory and the Electronic Structure of Atoms

Electronic Structure

Rice University

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University of Maryland - University College

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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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Calculate the frequency $(…

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Calculate the frequency (H…

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Calculate the frequency (h…

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Calculate the frequency of…

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Calculate the wavelength (…

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For an electron in a hydro…

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Calculate the energy and t…

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An electron in a hydrogen …

Okay, This question is asked, What is the frequency and wavelength of energy released as an electron drops from the fourth Quanta to the second quanta of a hydrogen atom? So we, uh, can use the equation. Yeah. The electron energy is able to plank's constant times frequency. Just be a fancy V with a version of this where the frequency is equal to 2.18 times 10 houthi negative 18th jewels divided by Plank's constant, which is 6.63 times 10 to the negative, 34th shoels per second. Okay, Big print sees one over the Quanta where it will say n final. So too square minus one over the N or Quanta initial, which is four. And then that's gonna be square. Okay, so flooding this all in, we get that the frequency of the emitted electromagnetic radiation, and in this case, it's light. Okay is equal to 6.17 times 10 to the negative. It's not negative. 10 to the 14th hurts, okay? And we know that it's not being hurts, because we look at this Jules divided by Jules per second. So that leaves us with inverse seconds. And this is a imager and this is an imager sore left with in verse seconds, which is also known as hurts. So we confined. So this is the frequency were also asked to find the wavelength. And we know that wavelength is related to frequency. By the equation, wavelength equals speed of light, divided by frequency where speed of light is three tough 0.0 times, 10 to the eighth meters per second, 10 to the eighth meters per second and the frequency which we just found 6.17 times 10 to the 14th hurts. So when we put this in, 14th hurts. So when we put this nor calculated week it that the wavelength is equal to 4.86 times 10 to the negative seventh meters, it's also equal to 400 a six centimeters. So this and this is why I knew the electromagnetic creation admitted was light because this isn't the visible light spectrum. Now they could release any kind of ah electromagnetic creation such as like gamma rays, which are really, really bad for you can be admitted, but they just have a much, much, much shorter wavelength and a much higher frequency. So here is the frequency and the wavelength of this is the frequency. And this is a way length of the emitted emit electromagnetic radiation as a electron of a hydrogen atom falls from the fourth Quanta down to these second Quanta. Thank you very much.

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