1. R Constant Of Helium
2. R Value Of Helium
3. Gas Constant Of Helium
4. Three Uses Of Helium
5. R Helium Balloons

Denoted by the symbol R, the value of the gas constant is: R = 8.314472 (15) J K-1 mol-1 The two digits in parentheses indicate the uncertainty (standard deviation) in the last two digits of the value. Movement of particles (atoms, molecules, or ions) in the gas phase. Helium is the second most abundant element in the universe, but here on earth, it's rather rare. Most people guess that we extract helium from the air, but actually we dig it out of the ground. Helium can be found in certain parts of the world, notably in Texas, as a. 1 moles Helium to grams = 4.0026 grams. 5 moles Helium to grams = 20.01301 grams. 10 moles Helium to grams = 40.02602 grams. 15 moles Helium to grams = 60.03903 grams. 20 moles Helium to grams = 80.05204 grams. 25 moles Helium to grams = 100.06505 grams. 30 moles Helium to grams = 120.07806 grams. 40 moles Helium to grams = 160.10408 grams. This book is divided into three chapters. The first chapter discusses the experimental results and compares with the equations used to generate the tables. These equations are supplemented by a vapor pressure equation, which represents the 1958 He-4 scale of temperature that is defined in terms of the vapor pressure of helium-4. Properties of Various Ideal Gases (at 300 K) Gas: Formula: Molar Mass: Gas constant: Specific Heat at Const. Specific Heat at Const.

Neils Bohr's model of the atom provided a wonderfully accurate explanation of thespectrum of hydrogen, but when it was applied to the spectrum of heliumit failed. Werner Heisenberg developed a modification of Bohr's analysis but it involvedhalf-integral values for the quantum numbers. Bohr considered non-integral values of quantum numbers nonsensical in terms of the logic of quantum theory. There was a crisis inquantum theory that ultimately led to the creation in the 1920's of the new quantumtheory which became known as quantum mechanics.

This is an attempt to apply the Old Quantum Physics to explaining the spectrum of helium. The energy level of an electronin an atom in which the effective charge is Z is −RZ²/n² where R is the Rydberg constant and n is the quantum number of the electron (its number of angular momentum units). The quantum number n is necessarily a positive integer, butZ can be either an integer or half-integer such as {1/2, 3/2, 5/2, … }.

To see how a half-integer value for Z can arise consider a unit negative charge distributed throughout a thin spherical shell of radius r.From a point within the shell; i.e., a point at a distance from the center of the shell less than r, the charge cancels out and the effect of the charge on the shell is zero. From a point whose distance for the center of the shell is greater than r the effectof the charge is the same as if it were concentrated at the center of the shell. Thus as distance from the center of the shell goesfrom a value greater than r to one less than r the effect charge goes from −1 to zero. Thus at a distance of exactly r theeffective charge has to −½. Thus for an electron in a shell the effect of the other electrons in the shell is thesame as if one half of the charge of the other electrons were concentrated at the center of the shell.

For the two electrons of a helium atom, if they have different quantum numbers and hence are in different shells the outer electronexperiences an effective charge in the nucleus of 2−1=+1 and the inner electron experiences an effective charge of 2−0=+2.But if the electrons have the same quantum number they both experience an effective charge in the nucleus of 2−½=+3/2.

Energy Levels

Let n₁ and n₂ be the quantum numbers of the two electrons in a helium atom. For simplicity assume thatn₁≥n₂. If n₁>n₂ then the energy levels of the electrons are

−R(2−1)²/n₁²
and
−R(2−0)²/n₂²
thus the total is
−R[1/n₁² + 4/n₂²]

If n₁=n₂ then the energy levels are both

−R(2−½)²/n₁²
so the total is
−2R(9/4)/n₁² = −(9/2)/n₁².

Energy Level Changes

For the case in which n₁>n₂ and n₁ is reduced to n₃ but n₃>n₂the energy change is

ΔE = R[1/n₃² − 1/n₁²]

This portion of the spectrum would be the same as for hydrogen.

For n₁>n₂ and n₂ is reduced to n₄ the energy change is

ΔE = R[4/n₄² − 4/n₁²] = 4R[1/n₄² − 1/n₁²]

R Constant Of Helium

The transition of an outer electron from quantum number n₁>n₂ to n₂ involves anenergy change of

−R(9/2)/n₂² − [ −R(1/n₁² + 4/n₂²)]
which is equal to
R[(4−9/2)/n₂² + 1/n₁²)] = R[1/n₁² − ½/n₂²]

The transition of an electron from quantum number n₂=n₁ to n₄<n₁involves an energy change of

−R[1/n₁² + 4/n₄²] − [− R(9/2)/n₁²]
or, equivalently
R[(9/2−1)/n₁² − 4/n₄²] = R[(7/2)/n₁² − 4/n₄²]

Finally there is the case in which the quantum number of the outer electron changes from n₁>n₂ ton₃ which is less than n₂.The energy change is

ΔE = −R(1/n₂+4/n₂²) − [−R(1/n₁² + 4/n₂²)]
or
R[(4−1)/n₂² + (1/n₁² − 4/n₃²)]
R[3/n₂² + 1/n₁² − 4/n₃²]

R Value Of Helium

There are thus five cases. If the helium model is valid then for any spectral line of helium there should exist integersolutions for at least one of the five cases.

The Helium Spectrum

There are three spectral lines for helium, {438.793 nm, 443.755 nm, 447.148 nm} for which the best explanation is a transition of an electron from quantum number 5 to quantum number 2 while the other electron remains at quantum number 1. The wave length is given by the equation

ΔE = hc/λ = R(1/n₃² − 1/n₁²)
hence
1/λ = (R/hc)(1/n₃² − 1/n₁²)

The value of the coefficient (R/hc) is 1.097373×10⁷ m⁻¹. If n₁=5 and n₃=2 then thewavelength for the transition should be 433.937 nm. For the spectral line at 438.793 this is in error by aboutr 1.1 percent.For the other two lines the computed value is in error by 2.3 and 3.0 percent, respectively.

Gas Constant Of Helium

For the 471.314 nm, 492.193 nm and 501.5675 nm spectral lines the closest fit is for n₁=4 and n₃=2 withn₂=1. For this transition the wavelength should be 486.009 nm. For the 471.314 nm line the computed value is 3.1 percent too high. For the 492.193 nm and 501.5675 nm lines the computed values are 1.3 percent and 3.2 percent too low.

Another line of the helium spectrum is at 667.815 nm. The best explanation for this line is a transition from n₁=3 to n₃ Questtech driver download. =2. The computed wavelength for this transition is 656.112 nm, an error of 1.8 percent.

Three Uses Of Helium

Here are these results in tabulated form:

R Helium Balloons

Unfortunately there is no readily available computations of the Helium spectrum using the New Quantum Theory (Quantum Mechanics)for comparison.