How Do You Calculate the Wavelength of an Electron Transition in a Helium Ion?

In summary, the He+ ion consists of an alpha particle nucleus and an orbiting electron, giving it a net positive charge. For part a), the expression for the electron state energies is E=(-4R)/(n^2) where R is the Rydberg constant. In part b), we can use the equation ΔE = RchZ²{1/n²(1) - 1/n²(2)} to find the wavelength associated with a transition between the lowest two energy states. This equation takes into account the Rydberg constant, the speed of light, Planck's constant, the nuclear charge, and the principal quantum numbers of the electron transition.
  • #1
amit25
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Homework Statement



He+ ion consists of a nucleus which is an alpha particle plus one orbiting electron.Hence it has a net positive charge.
a)Derive an expression for the electron state energies
b)what is the wavelength associated with a transition between the lowest two energy states?

Homework Equations


The Attempt at a Solution


For part a) i figured it out to be E=(-4R)/(n^2) where R is the rydbergs constant
for part b) I am having trouble not sure where to begin
 
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  • #2
Don't forget, the wavelength of a photon emitted, for a drop in energy level, is proportional to the difference in energies between the two levels.

I think that will be useful.
 
  • #3
should i use this

ΔE = RchZ²{1/n²(1) - 1/n²(2)}

where R is the Rydberg constant (1.0974 x 10E7 m-¹); c the speed of light in vacuum (2.9979 x 10E8 m s-¹); h Planck's constant (6.626 x 10E-34 J s); Z nuclear charge; n(1) & n(2) are the principal quantum numbers of the electron transition
 

Related to How Do You Calculate the Wavelength of an Electron Transition in a Helium Ion?

1. What is the Bohr model of the Helium atom?

The Bohr model of the Helium atom is a simplified representation of the Helium atom proposed by Niels Bohr in 1913. It describes the Helium atom as having a nucleus containing two protons and two neutrons, orbited by two electrons in specific energy levels or shells.

2. How does the Bohr model explain the stability of the Helium atom?

The Bohr model explains the stability of the Helium atom by proposing that the two electrons in the atom's outermost shell have a stable configuration, known as the duplet, with two electrons in the s orbital. This configuration satisfies the octet rule and makes the Helium atom less reactive.

3. What is the significance of the energy levels in the Bohr model of the Helium atom?

The energy levels in the Bohr model of the Helium atom represent the different allowed energy states of the electrons in the atom. These levels are quantized, meaning that the electrons can only exist in specific energy levels and cannot exist in between them. The energy levels determine the electron's energy and its distance from the nucleus.

4. How does the Bohr model explain the emission spectrum of Helium?

The Bohr model explains the emission spectrum of Helium by proposing that the electron can jump from one energy level to another by absorbing or emitting a precise amount of energy. When the electron jumps from a higher energy level to a lower one, it emits energy in the form of light, creating a unique emission spectrum for each element.

5. What are the limitations of the Bohr model of the Helium atom?

The Bohr model has several limitations, including its inability to explain the fine details of atomic structure and the behavior of atoms with more than one electron. It also does not account for the wave-like behavior of electrons, and it does not accurately predict the energy levels of heavier elements. These limitations were addressed by the development of quantum mechanics, which provides a more comprehensive understanding of atomic structure.

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