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A certain pitcher's fastballs have been clocked at about $100 \mathrm{mph} .$ (a) Calculate the wavelength of a 0.141-kg baseball (in nm) at this speed. (b) What is the wavelength of a hydrogen atom at the same speed? (1 mile $=1609 \mathrm{m} .)$

(a) $1.05 \times 10^{-25} \mathrm{mm}$(b) $8.88 \mathrm{mm}$

Chemistry 101

Chapter 7

Quantum Theory and the Electronic Structure of Atoms

Electronic Structure

Carleton College

Drexel University

University of Maryland - University College

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, So in this problem, we need to use the broke, please wavelength equation, which is represented by wait the equation. Wavelength equals plank's constant writing by mass times velocity. So they give us the velocity of the baseball to be 100 MPH and the mass to be 0.14 kilograms. So we need to convert 100 MPH. We need to convert that two meters per second show, say 100 MPH. First, we're gonna convert. Drop big line here. First, we're gonna convert that into kilometers. So one mile, it's equal to one point six one kilometers and one kilometer is equal to 1000 meters. So now we're in meters per hour. If we were to stop here, so we need to say so in in one hour there would be 3600 seconds. So we're gonna put one hour in top 3600 seconds, and we would get him, put it in the calculator speed to be 44 0.72 meters per second. So when we put this into the equation, we get 6.63 times 10 to the negative 34th. This is the plank's constant Jules, per second, divided by the Mass, is 0.1 for one kilograms, and the speed is 44 0.72 meters percent. So when we put that into the calculator, it's gonna end up being 1.5 times 10 to the negative 25th nanometers. So an incredibly small wavelength, Which makes sense because this is a large object. So second part of question asked what would be the wavelength of a hydrogen atom at the same speed, so we would just plug in the same numbers this 0.63? Well, no, it's times 10 to the fourth, the mass. You can either look it up or you can do the math on the mass is 1.66 times 10 to the negative 27th kilograms for one atom of hydrogen. It's very, very a small amount, and then the same speed 34 point seven to and when we plug Oh, that and the wavelength of a hydrogen atom traveling the same speed of the baseball and so being eight 0.88 millimeters or well say millimeters or zero point 0088 meters or 888 if you need significant figures. So this is a wavelength of a hydrant, Adam at the same speed of the baseball. This is the wavelength of the baseball, okay?

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