Units in quantum mechanical problem about 4-He

In summary, the units of the problem are chosen such that KB = 1 and ħ = 1, resulting in energies being expressed in Kelvin and lengths in Å. However, this is not sufficient to define a set of units as it still leaves the choice of mass or time units. The professor states that the value of ħ2 / 2m for a 4-He atom is 6.0599278, which can be achieved by setting the unit of mass as approximately 8.055 x 10^-26 kg. The use of ħ = 1 is not necessary in this scenario.
  • #1

Homework Statement


Units of the problem are chosen to be such as KB = 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!
 
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  • #2
Edit: Found it
Just multiply and divide by constants until the units are right.
 
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  • #3
physicsisgreat said:
Units of the problem are chosen to be such as KB = 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. kB = 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 kB = 1 is usually used the other way around: it allows to express temperature using units of energy.

physicsisgreat said:
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?

 
  • #4
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 KB = 1 to use K instead of J and then use Å instead of m. Right? :)
Thank you again! ^ ^
 
  • #5


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.
 

1. What are the units used in quantum mechanical problems about 4-He?

The units used in quantum mechanical problems about 4-He are typically in atomic units, which are a system of natural units commonly used in atomic and molecular physics. In this system, the unit of length is the Bohr radius, the unit of energy is the Hartree, and the unit of mass is the electron mass.

2. How do atomic units relate to SI units?

The conversion factor between atomic units and SI units is given by the following equations:
1 atomic unit of length = 0.529177 Ångstroms
1 atomic unit of energy = 27.2114 electronvolts
1 atomic unit of mass = 9.10938356 × 10^-31 kilograms

3. Why are atomic units commonly used in quantum mechanical problems?

Atomic units are commonly used in quantum mechanical problems because they simplify the equations and calculations involved. By using natural units that are specific to the system being studied, the equations can be written in a more compact and elegant form, making them easier to solve and interpret.

4. How do atomic units affect the results of calculations?

Atomic units do not affect the results of calculations, as they are simply a different system of units. The values of physical properties and quantities will be the same regardless of what units are used, as long as the conversion between units is done correctly.

5. Are there any other commonly used units in quantum mechanical problems about 4-He?

In addition to atomic units, some other commonly used units in quantum mechanical problems about 4-He include the Rydberg energy (which is equal to two times the Hartree energy) and the Rydberg constant (which is equal to half the Hartree energy divided by the Bohr radius). These units are often used when studying the energy levels and transitions of helium atoms.

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