Question

An electron is in the n = 9 level of ionized helium. (a) Find the longest wavelength that is emitted when the electron makes a transition from the n = 9 level to a lower level. um (b) Find the shortest wavelength that can be emitted. um (c) Find the longest wavelength at which the electron in the n = 9 level will absorb a photon and move to a higher state, if we could somehow keep it in that level long enough to absorb. um (d) Find the shortest wavelength that can be absorbed. um

Answer 1

these are standard formula i am using so u can use them directly in your exam

a)

ΔE = -13.6 eV *Z² * ( 1/n₁² - 1/n₂2 )  

= -13.6*2^2 *( 1/9^2-1/8^2) = 0.178 eV

ΔE =hc/λ

so less energy more wavelength

λ = hc/ΔE = 1243*10^-9/ 0.178 = 6.98314607e-6 m = 6.98314607  μm

B)

ΔE = 13.6*4*80/81 =  53.7283951eV

λ = hc/ΔE = 1243*10^-9/ 53.7283951 =2.31348805e-8

= 0.02313 μm

C)

ΔE = -13.6 eV *Z² * ( 1/n₁² - 1/n₂2 )  

= -13.6*2^2 *( 1/9^2-1/10^2) = 0.127604938 eV

λ = hc/ΔE = 1243*10^-9/0.127604938 =9.74100234e-6 = 9.74100μm

D)

ΔE = -13.6 eV *Z² * ( 1/n₁² - 1/n₂2 )  

= -13.6*2^2 *( 1/9^2-1/∞^2)

=

0.672 eV

λ = hc/ΔE = 1243*10^-9/0.672 = 1.85  μm

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