(adsbygoogle = window.adsbygoogle || []).push({}); this problem is killing me!! [calculation of electron transition]

i've been trying to solve this problem.. the answer should be 7.. my answer is 0.7 !!

What is the value of n_i for an electron that emits a photon of wavelength 93.14 nm when it returns to the ground state in the H atom?

my solution..

n_f=1

λ=93.14 nm×(10^(-9) m)/(1 nm)=93.14×10^(-9) m

∆E=hν=hc/λ=(6.63×10^(-34)×3.00×10^8)/(93.14×10^(-9))≈2.14×10^(-18)

∆E=-2.18×10^(-18) (1/(n_f^2 )-1/(n_i^2 ))

2.14×10^(-18)=-2.18×10^(-18) (1/1^2 -1/(n_i^2 ))

-2.14/2.18=1-1/(n_i^2 )

1.982= 1/(n_i^2 )

n_i^2=0.5045

n_i=√0.5045≈0.7

n_i = n initial

n_f = n final

λ = wavelength ( lambda )

∆E = energy of the transition

h = plank's constant

ν = frequency ( nu )

c = speed of light

if reading the solution is an issue.. just past it in microsoft word and activate the equation mode..

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# This problem is killing me [calculation of electron transition]

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