Consider a Hydrogen atom in the 3rd excited state (n = 4). The maximum wavelength of light that can be emitted is 9.7 x 10^-8 m 1.9 x 10^-6 m 1.03 x 10^-7 m 2.5 x 10^-5 m

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asked Apr 16, 2021 133k views

1 Answer

Andrej Herich · Answer 1 · 2021-04-21T17:20:50+0000

Answer: The maximum wavelength of light that can be emitted is

Step-by-step explanation:

$E=(hc)/(\lambda)$

$\lambda$ = Wavelength of radiation

E= energy

For wavelength to be maximum, energy would be minimum, i.e the electron will jump from n=4 level to n =3

Using Rydberg's Equation:

$(1)/(\lambda)=R_H\left((1)/(n_i^2)-(1)/(n_f^2) \right )* Z^2$

Where,

R_H = Rydberg's Constant =
1.097* 10^7m^(-1)

n_f = Higher energy level = 3

n_i = Lower energy level = 4

Z= atomic number = 1 (for hydrogen)

$(1)/(\lambda)=1.097* 10^7\left((1)/(3^2)-(1)/(4^2) \right )* 1^2$

$(1)/(\lambda)=0.053* 10^7$

$\lambda=1.9* 10^(-6)m$

Thus the maximum wavelength of light that can be emitted is