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An orange emission line is observed at 656.3 nm in the hydrogen emission spectrum. Determine the initial energy level of the electron.

Respuesta :

The energy of a wave is calculated by E = hf where f is the frequency and h is the Planck's constant (6.626 ×10^-34 J/s).
The formula may be written as E= hc/λ where c is the speed of light 3×10^8 m/s and λ is the wavelength.
Thus energy = (6.626 × 10^-34)×(3 ×10^8)/ (656.3 nm)
                     =  3.0267 × 10^ -19 J
 Therefore, the initial energy level of an electron is 3.0267 × 10^-19 joules.
pstnonsonjoku

The initial energy level of the electron is n=3.

The emission line at 656.3 nm in the hydrogen emission spectrum corresponds to the Balmer series hence;

λ = 656.3 × 10^-9 m

nfinal = 2 (Balmer series)

ninitial = ?

R = 1.097 × 10^7 m-1

From;

1/λ = R(1/n^2final - 1/n^2initial)

Substituting values;

1/656.3 × 10^-9 = 1.097 × 10^7 (1/2^2 - 1/n^2initial)

0.1389 = 0.25 -  1/n^2initial

1/n^2initial = 0.25 - 0.1389

ninitial = 3

Hence, the initial energy level of the electron is n=3.

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