ShmoopTube

00:00

Thank you We speak and here's your shmoop du jour

00:05

brought to you by evil genius which reminds us by

00:08

using schmuck you hereby agree to use any and all

00:10

knowledge acquired solely for the good of mankind And you

00:13

declined all opportunities becoming evil genius dr evil and mini

00:17

me or accelerating an electron through a potential difference in

00:20

a diffraction experiment they determined that the debra lee wavelength

00:23

of the electron is sixty six point three pico meters

00:27

austin powers international man of mystery let's Find the value

00:31

of that potential difference in orderto foil their evil plan

00:34

and save the world Which of the following is the

00:37

correct value And here are your options Right Right there

00:41

Okay well we're not sure how one accelerating electrons health

00:45

doctor It'll conquered the globe But then again we didn't

00:47

go to six years in evil medical school So what

00:50

do we know Well we do actually know something about

00:53

too early wave lengths to really help prove that all

00:55

that franz show the properties of waves as well as

00:58

the properties of particles He came up with a formula

01:01

stating that the wavelength of an electron equals planks constant

01:04

Divided by the electrons momenta And we know that momentum

01:08

equals mass times velocity so we can rewrite the equation

01:11

accordingly When we hear the phrase and electrons accelerated through

01:15

a potential difference we think Huh But we should be

01:19

thinking of electron volts One electron volt equals the amount

01:24

of kinetic energy gain by a single electron wanted accelerate

01:28

through an electric potential difference of one full A single

01:32

electron volt equals one point six times ten to the

01:35

negative nineteen Jules do the conservation of energy You know

01:39

that the kinetic energy of the electron equals the potential

01:41

difference required to accelerate it We can use the formula

01:45

for kinetic energy to find a potential difference Kinetic energy

01:48

goes one half mass times the square of velocity And

01:52

we know the mass of an electron in just nine

01:53

point one one times ten to the negative thirty one

01:55

kilograms But we just need to solve her velocity Remember

01:59

our earlier equation for the wavelength one that said wavelength

02:03

equals planks constant over mass times velocity of that one

02:08

By rearranging this we can find an equation for velocity

02:11

Velocity equals planks constant over mass times wailing We can

02:15

solve this equation into the kinetic energy equation can simplify

02:19

things a little bit further to go And now it's

02:23

Time for numbers Thanks constant is six point six three

02:27

times ten to the negative Thirty fourth jules seconds a

02:30

mass of an electron Is nine point one one times

02:32

ten to the negative thirty first and the wavelength is

02:35

sixty six Point three Pico meters are equation Looks like

02:38

this this ugly thing right there doing the math we

02:42

find with the kinetic energy of the electron equals five

02:44

point four nine times ten to the negative seventeen jewels

02:47

But remember we need to find the potential difference So

02:50

we need to divide this result by the value of

02:52

an electron volt find the voltage We do that and

02:55

we get our potential difference of three hundred forty three

02:57

electrons Bowls correct answer is and after questions like this

03:02

we wonder who has the time to be an evil

03:03

genius Yeah we're in all this stuff and come up

03:06

with a plan to rule the world really where these 00:03:08.36 --> [endTime] keys in them

Full Transcript