 ## General Chemistry

Learn the toughest concepts covered in Chemistry with step-by-step video tutorials and practice problems by world-class tutors

9. Quantum Mechanics

# De Broglie Wavelength

The De Broglie Wavelength equation relates wavelength to velocity or speed.

De Broglie Wavelength
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concept

## De Broglie Wavelength 58s
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now the day broadly wavelength associates the wave nature of a moving object with its velocity through plank's constant. Now, when we say object, this is a photon, a subatomic particle or literally anything with a velocity. Now here we have our de Broglie wavelength formula here. We're going to say that this formula is used when we have the velocity and wavelength of an object. So here we're going to say that wavelength, which is represented by Lambda in Meters, equals plank's constant, which is equal to 6.626 times 10 to the negative jewels, time seconds divided by mass of the object in kilograms times the velocity in meters per second. So just realize here that based on the formula, the wavelength of an object is going to be inversely proportional to its mass and velocity.
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example

## De Broglie Wavelength Example 1 1m
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So here we have to find the wavelength of a proton with the speed of 6. times 10 to the 5 m per second. Here, the mass of a proton is recorded as 1.67 times, 10 to the negative 27 kg. Alright, so it's going to be wavelength equals plank's constant divided by mass times velocity. Now remember here that plank's constant is Jules Times seconds and what we need to realize here is that Jewell one Jewell is equal to kilograms times meter squared over second squared. So if we're doing Jules time seconds, that really means kilograms times meter squared over second squared times seconds. So here, one of these seconds will cancel out with this second. So the units for plants constant would be 6.626 times 10 to the negative, 34 kilograms times meter squared over seconds. We do this to see how the kilograms of my subatomic particle in this case can cancel out. So we have 1.67 times 10 to the negative 27 kg and it's traveling at a velocity of 6.25 times 10 to the 5 m per second. So here what cancels out our meters, cancels out with meters and then we're gonna have here seconds. Cancel out with seconds kilograms, cancel out with kilograms. So we're gonna have 1 m left. So when we plugged that into our calculator will get 6. times 10 to the negative 13 m for our wavelength off our proton within this question
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Problem

What is the velocity (in m/s) of an electron that has a wavelength of 3.13 x 105 pm? (Mass of an electron = 9.11 x 10-31 kg).

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Problem

The faster an electron is moving, the _________ its kinetic energy, and the __________ its wavelength.

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Problem

Consider an atom traveling at 1% the speed of light. The de Broglie wavelength is found to be 7.1316 x 10-39 m. Which element is this? 