# AP Physics 2: 1.4 Probability and Systems

AP Physics 2: 1.4 Probability and Systems. Which of the following is the correct value?

AP Physics 2 | Probability and Systems |

Language | English Language |

Science Practice 1 | Using representations and models |

### Transcript

me or accelerating an electron through a potential difference in

a diffraction experiment they determined that the debra lee wavelength

of the electron is sixty six point three pico meters

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

of that potential difference in orderto foil their evil plan

and save the world Which of the following is the

correct value And here are your options Right Right there

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

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

go to six years in evil medical school So what

do we know Well we do actually know something about

too early wave lengths to really help prove that all

that franz show the properties of waves as well as

the properties of particles He came up with a formula

stating that the wavelength of an electron equals planks constant

Divided by the electrons momenta And we know that momentum

equals mass times velocity so we can rewrite the equation

accordingly When we hear the phrase and electrons accelerated through

a potential difference we think Huh But we should be

thinking of electron volts One electron volt equals the amount

of kinetic energy gain by a single electron wanted accelerate

through an electric potential difference of one full A single

electron volt equals one point six times ten to the

negative nineteen Jules do the conservation of energy You know

that the kinetic energy of the electron equals the potential

difference required to accelerate it We can use the formula

for kinetic energy to find a potential difference Kinetic energy

goes one half mass times the square of velocity And

we know the mass of an electron in just nine

point one one times ten to the negative thirty one

kilograms But we just need to solve her velocity Remember

our earlier equation for the wavelength one that said wavelength

equals planks constant over mass times velocity of that one

By rearranging this we can find an equation for velocity

Velocity equals planks constant over mass times wailing We can

solve this equation into the kinetic energy equation can simplify

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

Time for numbers Thanks constant is six point six three

times ten to the negative Thirty fourth jules seconds a

mass of an electron Is nine point one one times

ten to the negative thirty first and the wavelength is

sixty six Point three Pico meters are equation Looks like

this this ugly thing right there doing the math we

find with the kinetic energy of the electron equals five

point four nine times ten to the negative seventeen jewels

But remember we need to find the potential difference So

we need to divide this result by the value of

an electron volt find the voltage We do that and

we get our potential difference of three hundred forty three

electrons Bowls correct answer is and after questions like this

we wonder who has the time to be an evil

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

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