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

AI Thread Summary
To calculate the wavelength of an electron transition in a helium ion (He+), the expression for electron state energies is derived as E = (-4R)/(n^2), where R is the Rydberg constant. For the wavelength associated with a transition between the lowest two energy states, the energy difference ΔE can be calculated using the formula ΔE = RchZ²(1/n²(1) - 1/n²(2)). This equation incorporates the constants R, c, and h, along with the nuclear charge Z and the principal quantum numbers n(1) and n(2). The wavelength of the emitted photon is inversely proportional to the energy difference between the two levels. Understanding these relationships is crucial for solving the problem.
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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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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.
 
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
 
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