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A helium ion is at rest in a laboratory when it is put in an electric field of E=2 N/C. An infrared light, of wavelength 2000 nm, is directed towards the ion. The ion is moving towards the source of radiation. After what time in the laboratory frame in seconds will the ion absorb the infrared radiation?

Details and assumptions
The first absorption line of helium at rest occurs at a wavelength of λ0=1083 nm.
The mass of the helium atom (approximately the same as of the Helium ion) is 6.65×10−27 kg.
Only one electron is taken from the helium atom to make it into an ion.
Neglect radiative losses due to acceleration.
You may neglect any relativistic effects in the acceleration of the ion, but not otherwise

The charge of He ion = e
The aceleration of ion in the electric field
ma=eE
a=eE/m
KE=mv²/2= m(at)²/2=
= (eEt)²/2m
ℇ=KE
ℇ = hc/λ
hc/λ=(eEt)²/2m
t={sqrt(2mhc/λ)}/eE=
={sqrt(2•6.65•10⁻²⁷•6.63•10⁻³⁴•3•10⁸/1083•10⁻⁹)}/1.6•10⁻¹⁹•2=
=1.5•10⁻⁴ s

wrong

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