Units in quantum mechanical problem about 4-He

[physicsisgreat]

Homework Statement

Units of the problem are chosen to be such as K_B = 1 and ħ = 1 so that energies are expressed in Kelvin and lengths in Å. The professor says the resulting value of ħ² / 2 m for a 4-He atom is 6.0599278: how is that possibile?

Homework Equations

Natural units websites give many conversion factors:
https://thespectrumofriemannium.wordpress.com/2013/01/30/log070-natural-units/
http://en.wikipedia.org/wiki/Natural_units

The Attempt at a Solution

as the 4-He mass is
m ≈ 6 * 10^-27 Kg
ħ² / 2 m ≈ 8,4 * 10^^-43 m²/s
Now using conversions of meters and seconds to eV (given at https://thespectrumofriemannium.wordpress.com/2013/01/30/log070-natural-units/) we find
m²/s ≈ 0,0169
so the result is wrong.

I tried in many other ways, starting for example from ħ = 1 and converting the 4-He mass, but I cannot find any way to get the result
ħ² / 2 m ≈ 6.0599278

Thank you very much in advance for your help!

 

[mfb]

Edit: Found it
Just multiply and divide by constants until the units are right.

 

[DrClaude]

Units of the problem are chosen to be such as K_B = 1 and ħ = 1 so that energies are expressed in Kelvin and lengths in Å.

That's not sufficient to define a set of units. k_B = 1 only sets the temperature scale, and [ħ] = [M][L]²[T]^-1, so you can still set any two out of mass, length, and time. If you take Å as the unit of lenght, that leaves mass or time.

By the way, setting k_B = 1 is usually used the other way around: it allows to express temperature using units of energy.

The professor says the resulting value of ħ² / 2 m for a 4-He atom is 6.0599278: how is that possibile?

By setting the units of mass as ##\approx 8.055 \times 20^{-26}\ \mathrm{kg}##, which is a bit weird. Maybe time is set by some other constant?

 

[physicsisgreat]

Thank you very much for your replies!
So it seems like the information ħ = 1 is actually not needed at all: if I get it right, we just use K_B = 1 to use K instead of J and then use Å instead of m. Right? :)
Thank you again! ^ ^

 

[paranormal]

I would first check the calculation steps and make sure that all units are converted correctly. It is possible that there may be a mistake in the conversion factors used or in the units themselves.

I would also double check the given value of ħ2 / 2 m for a 4-He atom and make sure it is accurate. If the value is indeed incorrect, I would bring it to the attention of the professor and ask for clarification or correction.

Additionally, I would explore other sources and references to see if there are any alternative ways of obtaining the value of ħ2 / 2 m for a 4-He atom. This can help confirm if the given value is correct or if there is a mistake in the calculation.

Finally, I would also consider the possibility that the given value may be an approximation or an experimental value with some margin of error. In this case, it may be helpful to discuss with the professor or consult other experts in the field to determine the significance of the error and if it is within an acceptable range.