## Sapling week 2/3

$H_{\psi }=E_{\psi }$

1-D: $E_{TOTAL}\psi (x)=E_{k}\psi (x)+V(x)\psi(x)=-\frac{h^{2}}{8\pi ^{2}m}\frac{d^{2}\psi(x)}{dx^{2}}+V(x)\psi(x)$

Jessica Katz 1G
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### Sapling week 2/3

Should we be able to answer this question already? If so does anyone know the steps to solve it? Any help would be great. Thanks!

What is the minimum uncertainty in an electron's velocity (Δvmin) if the position is known within 15 Å.

What is the minimum uncertainty in a helium atom's velocity (Δvmin) if the position is known within 1.2 Å.

DanielHong2L
Posts: 39
Joined: Wed Sep 30, 2020 9:51 pm

### Re: Sapling week 2/3

Jessica Katz 1G wrote:Should we be able to answer this question already? If so does anyone know the steps to solve it? Any help would be great. Thanks!

What is the minimum uncertainty in an electron's velocity (Δvmin) if the position is known within 15 Å.

What is the minimum uncertainty in a helium atom's velocity (Δvmin) if the position is known within 1.2 Å.

Intedeterminancy Equation = delta momentum * delta position >/= h/4pi

h/4pi is a constant; delta position is the 15 angstroms; delta momentum = mass of electron * velocity
- you know mass of electron (9.1*10^-31 kg); so you could figure out veloicty of electron

For helium change the mass to mass of helium atom (I believe this should still work)

Lmk if you have more questions!

David He
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### Re: Sapling week 2/3

DanielHong2L wrote:
Jessica Katz 1G wrote:Should we be able to answer this question already? If so does anyone know the steps to solve it? Any help would be great. Thanks!

What is the minimum uncertainty in an electron's velocity (Δvmin) if the position is known within 15 Å.

What is the minimum uncertainty in a helium atom's velocity (Δvmin) if the position is known within 1.2 Å.

Intedeterminancy Equation = delta momentum * delta position >/= h/4pi

h/4pi is a constant; delta position is the 15 angstroms; delta momentum = mass of electron * velocity
- you know mass of electron (9.1*10^-31 kg); so you could figure out veloicty of electron

For helium change the mass to mass of helium atom (I believe this should still work)

Lmk if you have more questions!

Thanks for your clarification, but where should I find the weight of helium atom ?

Joseph Hsing 3H
Posts: 35
Joined: Wed Sep 30, 2020 9:42 pm

### Re: Sapling week 2/3

You can find the molar mass of a Helium atom on the periodic table: 4.002 g/mol. Since we are using Joules with Planck's constant, convert grams to kilograms, so 4.002 x 10^-3 kg. And make sure to multiply by Avogadro's number so 6.002 x 10^23 He atoms/mol in this question so that you get the value for just one He atom.

MCalcagnie_ 2H
Posts: 31
Joined: Wed Sep 30, 2020 10:08 pm

### Re: Sapling week 2/3

Hi!! First off, this was really helpful for me, I have been stuck on that problem for a while now only to realize it was a conversion issue. Second, I was wondering if anyone knew how to solve #4 on Sapling "When a metal was exposed to photons at a frequency of 1.32×1015 s−1,
electrons were emitted with a maximum kinetic energy of 3.50×10−19 J." ? I thought I understood it, but I keep getting it wrong.

John Calonia 2F
Posts: 36
Joined: Wed Sep 30, 2020 9:49 pm

### Re: Sapling week 2/3

This is a photoelectric effect question. You would enter in your known values for frequency and kinetic energy to find the work function I assume. That would lead you with 3.50×10−19J=(6.626x10^-34)(1.32×1015 Hz) - (work function). From there just solve for work function through algebra.

MCalcagnie_ 2H
Posts: 31
Joined: Wed Sep 30, 2020 10:08 pm

### Re: Sapling week 2/3

Okay perfect thanks John! What abut for part two of that question? Where do I get the other values? Do I use the work function from the first part or no because they are different frequencies?

asalest 2K
Posts: 41
Joined: Wed Sep 30, 2020 9:39 pm

### Re: Sapling week 2/3

for the first part, you regimen all the information needed to solve the equation using the uncertainty equation, just use the electron mass and don't forget to convert angstroms to m!
for the second one make sure you convert the molar mass of helium from g/mol to kg/atoms using avogadro's then solve using the uncertainty equation! make sure all your units are correct!!

Laura 3J
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### Re: Sapling week 2/3

You would just use Heisenberg's Indeterminacy equation but first convert Angstroms to meters.

Shrey Pawar 1A
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### Re: Sapling week 2/3

You can use the indeterminacy equation and fill in the mass as that of an electron or in the second case the molar mass of helium (in kg) multiplied by Avogadros. Then you can get the velocity. After this you can just use the KE = .5mv^2 and plug in. Hope this helps!

MCalcagnie_ 2H
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Joined: Wed Sep 30, 2020 10:08 pm

### Re: Sapling week 2/3

Thanks everyone, that cleared things up!

Lucy_Balish_1I
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Joined: Wed Sep 30, 2020 9:37 pm
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### Re: Sapling week 2/3

Joseph Hsing 3H wrote:You can find the molar mass of a Helium atom on the periodic table: 4.002 g/mol. Since we are using Joules with Planck's constant, convert grams to kilograms, so 4.002 x 10^-3 kg. And make sure to multiply by Avogadro's number so 6.002 x 10^23 He atoms/mol in this question so that you get the value for just one He atom.

Thank you so much for explaining this. It helped a lot and I feel better about how to solve this problem thanks to you!

Chinmayi Mutyala 3I
Posts: 34
Joined: Wed Sep 30, 2020 9:50 pm

### Re: Sapling week 2/3

Hi! This question has to do with Heisenberg Uncertainty/Indeterminacy principle.