Hydrogen gas absorbs light of wavelength 103 nm. Afterward, what

arbixerwoxottdrp1l 2022-04-07 Answered
Hydrogen gas absorbs light of wavelength 103 nm. Afterward, what wavelengths are seen in the emission spectrum?
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Answers (1)

Lea Johnson
Answered 2022-04-08 Author has 13 answers
Step 1
Let the absorbed wavelength by the hydrogen gas can be
λ = 103   n m
Therefore, the energy absorbed is
E = h c λ = ( 6.625 × 10 34 ) ( 3 × 10 8 ) ( 103 × 10 9 ) × ( 1 1.6 × 10 19 ) e V = 12.05   e V E = 12.05   e V
And the ground state energy of the hydrogen is -13.6 eV
Step 2
Therefore, to find the value of n we will use the following method
( 13.6 n 2 ) ( 13.6 1 2 ) = 12.05 n = 13.6 1.55 = 2.96 3 n = 3
Step 3
Therefore, the electron is jumping from n =3 to n = 1 and the corresponding wave lengths can be calculated as follows
Now the line corresponding to n 2 = 3 to n 1 = 1 is the first line , its wave length is maximum
That is,
1 λ m a x = R ( 1 1 2 1 3 2 ) = ( 1.1 × 10 7 ) ( 1 1 9 ) = 0.977 × 10 7 λ m a x = 1022   A ˚
Step 4
Similarly, the minimum wavelength is
1 λ m i n = R ( 1 1 2 1 2 ) = ( 1.1 × 10 7 ) ( 1 ) = 1.1 × 10 7 = 912 λ m i n = 912   A ˚
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