Achieve 2 Question 19

[KDeguzman_Dis3K]

"What is the minimum uncertainty in a helium atom's velocity (Δvmin) if the position is known within 1.1 Å."

For this question, I know we need to convert 1.1 angstroms to meters by multiplying 1.1 x 10^-10. To find the mass of a helium atom, I converted 4.002g to kg and multiplied by Avogadro's number and got 2.41 x 10^21.
In the end, using the Heisenberg equation, I got (6.626 x 10^-34)/ (2.41 x 10^21)(1.1 x 10^-10), but my answer is still incorrect on Achieve. Did I find the mass of the helium atom incorrectly?

[Lauren Woodward 1I]

When finding the mass of a helium atom, you should divide the molar mass by Avogadro's number. That would mean dividing the number of grams in one mole of Helium by the number of He atoms in a mole. Also, I'm not sure if you just omitted this while typing, but your final equation should have 4pi in the denominator.

[Qinyan Feng 1H]

Hi

4.002g is the molar mass of Helium, which means that is the mass of 1 mol Helium atoms. So in order to find the mass of a single Helium atom, you should divide 4.002 by the Avogadro's number. I think that is where your problem is.

[Hanyi Jia 3B]

You are given Δx = 1.1 Å, and you are asked to find Δv.
Then,
ΔpΔx ≥ h/4π
m_HeΔv≥ h/(4πΔx)
Δv≥ h/(4πm_HeΔx)

You made two mistakes:
1. m_He=(molar mass)_He/Avogadro's number, 2.41 x 10^21 is wrong. I can consider the unit of Avogadro's number as atoms/mol, while the unit of molar mass is grams/mol. (grams/mol)/(atoms/mol)=grams/atom.
2. Didn't calculate that 4π in your equation.

[masontsang]

Hi!

To solve this problem, I would first convert angstroms to meters (1.1 Å to 1.1 x 10^-10 m)! To find the mass of a Helium atom (in kg), I would divide the molar mass of Helium (which represents the mass of 1 mol of Helium and is given on the periodic table) by Avogadro's number and divide that number by 1000 to convert g to kg. Then, I would use the values we calculated and put them into the Heisenberg equation (Δp x Δx >= h/4π or rearranged as Δv >= h/[4π * Δx * m]) to get the correct answer!

I hope this helps!

[Arjan G 2H]

Hi! So for this problem, we are being asked to find a helium atom's uncertainty in velocity. Because we are using just a single Helium atom, we would need to divide the molar mass of helium by Avogadro's number to find the masa of a single helium atom. Then, we use the value we calculated for the value of "m" in the uncertainty equation. Then, we are given the change in position, which is 1 Angstrom, which we can convert to meters and plug it in for the value of "delta(x)." then, we multiply the mass of a helium atom by the value of "delta(x)" and then multiply that value by 4pi. Then, we divide Planck's constant, or h, by the product we get to find the uncertainty in the helium atoms velocity. I hope this helps!

[Madelyn_Rios_2c]

1) After converting 4.002g to kg, the m_He is the (mass of helium)/(avogadro's number).
2) After finding m_He, use the equation: Δv ≥ h/(4π * m_He * Δx)

[Rio Gagnon 1G]

Because we are looking at one He atom, we must use the molar mass in g/mol of He and divide (not multiply) it by avogadro's number (6.022 atoms/mol). Other than that, the only detail that you missed is that you must divide by 4 π , as the equation is Δv >= h/(4π*m*Δx).