Hydrogen atoms in a discharge tube are in their ground state. If a beam of free electrons of energy12.9 eV are fired at the hydrogen atoms in the discharge tube, (a) determine the maximum wavelength of the radiation that can be emitted by the hydrogen atoms, AND (b) determine the minimum wavelength of the radiation that can be emitted by the hydrogen atoms.

See explanation

Explanation:

-0.7ev = -13.6/n^2

n= 4

4--->1

4--->3, 3---> 2, 2--->1

E4-E1= -13.36(1/4^2 - 1/1^2) = 12.53 eV

E4-E3 = -13.36 (1/4^2 - 1/3^2) = 0.65 ev

E3-E2 = -13.36 (1/3^2 - 1/2^2) = 1.86 eV

E2- E1 = -13.6 ( 1/2^2 - 1/1^2) = 10.02 ev

a)

λ= 6.6 × 10^-34 × 3 × 10^8/12.53 × 1.6 × 10^-19

λ= 19.8 × 10^-26/20.048 ×10^-19

λ= 9.9 × 10^ -8 m

b)

λ= 6.6 × 10^-34 × 3 × 10^8/0.65 × 1.6 × 10^-19

λ= 19.8 × 10^-26/1.04 ×10^-19

λ= 19.0 × 10^ -7 m

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