## Uncertainty in Speed [ENDORSED]

$\Delta p \Delta x\geq \frac{h}{4\pi }$

Veronica_Lubera_2A
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### Uncertainty in Speed

The hydrogen atom has a radius of approximately 0.05 nm. Assume that we know the position of an electron to an accuracy of 1% of the hydrogen radius, calculate the uncertainty in the speed of the electron using the Heisenberg uncertainty principle.

So the correct answer is Delta V >= 10^8 m/s. How would you solve the question to receive this answer?

Chem_Mod
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### Re: Uncertainty in Speed  [ENDORSED]

I will be covering this topic in class during Week 2.

Calculate 1% of the hydrogen radius (0.05 nm) in meters and use it as the uncertainty in position, delta x, of the electron in the Heisenberg Indeterminacy (Uncertainty) Equation.

Sears 4A
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### Re: Uncertainty in Speed

I do not think we are covering this until week 2, and the week 2 homework can be from review or quantum, so maybe wait until Dr. Lavelle goes over this in lecture!

AnayaArnold_3L
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### Re: Uncertainty in Speed

Veronica_Lubera_1A wrote:The hydrogen atom has a radius of approximately 0.05 nm. Assume that we know the position of an electron to an accuracy of 1% of the hydrogen radius, calculate the uncertainty in the speed of the electron using the Heisenberg uncertainty principle.

So the correct answer is Delta V >= 10^8 m/s. How would you solve the question to receive this answer?

Dr.Lavelle will more than likely go over this concept more in a lecture during week 2 so I wouldn't worry about it too much as of right now.

KatherineValdez_4B
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### Re: Uncertainty in Speed

I really hope he does cover it because I'm confused.

andrewcj 2C
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### Re: Uncertainty in Speed

I think it goes like this:
($\Delta$p)($\Delta$x) = (1/2)(h/2$\pi$)
($\Delta$p) = m($\Delta$v)
From here you can plug in (0.01)*(0.05 nm) for $\Delta$x and solve.

andrewcj 2C
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### Re: Uncertainty in Speed

One additional thing for my reply, make sure you convert nm to m.

nicole-2B
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### Re: Uncertainty in Speed

andrewcj 4I wrote:One additional thing for my reply, make sure you convert nm to m.

thanks for clarifying this.

melinak1
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### Re: Uncertainty in Speed

andrewcj 4I wrote:One additional thing for my reply, make sure you convert nm to m.

ohh ok thank you!

KatherineValdez_4B
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### Re: Uncertainty in Speed

andrewcj 4I wrote:One additional thing for my reply, make sure you convert nm to m.

Thanks for this I almost forgot to do it.

Aprice_1J
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### Re: Uncertainty in Speed

Another important conceptual thing to think about is that the more you know about the position of an electron, the less we know about its velocity- they have an inverse relationship.

Anvi Brahmbhatt 4A
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### Re: Uncertainty in Speed

andrewcj 4I wrote:I think it goes like this:
($\Delta$p)($\Delta$x) = (1/2)(h/2$\pi$)
($\Delta$p) = m($\Delta$v)
From here you can plug in (0.01)*(0.05 nm) for $\Delta$x and solve.

Thank you for the explanation!

Claire Stoecklein 1E
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### Re: Uncertainty in Speed

When you determine delta p for the indeterminacy equation, make sure to use p=mv, using the velocity given in the equation and the mass of electron, 9.109 x 10^-31.

brennayoung
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### Re: Uncertainty in Speed

This equation can be used for other atoms than hydrogen right?

Ruth Glauber 1C
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### Re: Uncertainty in Speed

I think you need to calculate 1% of the hydrogen radius (0.05 nm) in meters for the uncertainty.

Caitlin Ciardelli 3E
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### Re: Uncertainty in Speed

Another way to calc uncertainty in v:

10 ms^-1 +/- .5
You can take the +/- value and multiply it by 2. This is another way to find uncertainty in v

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### Re: Uncertainty in Speed

In response to Brennayoung's question, I believe that we will only be applying this to hydrogen for now. This principle is used when measuring position and momentum of a particle.

Sara Richmond 2K
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### Re: Uncertainty in Speed

Use these equations:
(delta p)(delta x) = (1/2)(h/4 PIE)
(deltap) = m( delta v)

Sometimes this type of problem can be confusing because they dont give you the delta p equation.

Also remember to multiply the delta v uncertainty by 2 because it is plus or minus a certain amount.

Mitchell Koss 4G
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### Re: Uncertainty in Speed

Also, don’t confuse frequency (v) with velocity (v)