The ground state energy of hydrogen atom is - 13.6 eV.
(i) What is the potential energy of an electron in the 3rd excited state?
(ii) If the electron jumps to the ground state from the 3rd excited state, calculate the wavelength of the photon emitted.

Solution

The energy of an electron in nth orbit is given by, $E_{n} = - \frac{13.6}{n^{2}} eV$

(i) For 3rd excited state, n = 4

$∴$ Energy at the third excited level is given by,

$E_{4} = - \frac{13.6}{4^{2}} = - \frac{13.6}{16} = - 0.85 eV$

(ii) Required energy to jump electron to the ground state from the 3rd excited state is,

$E = E_{4} - E_{1}$

$= - \frac{13.6}{4^{2}} - (- \frac{13.6}{1^{2}}) = - 0.85 + 13.6 = 12.75 eV$

∴ Wavelength of the photon emitted is,

$λ = \frac{hc}{E} ∵ E = \frac{h c}{λ}$

$\Rightarrow$ $λ = \frac{6.63 \times 10^{- 34} \times 3 \times 10^{8}}{12.75 \times 1.6 \times 10^{- 19}}$

$= \frac{19.878 \times 10^{- 7}}{20.4} = 0.974 \times 10^{- 7} = 974 Å .$
is the wavelength of the photon emitted.

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Wave Optics

The ground state energy of hydrogen atom is - 13.6 eV.
(i) What is the potential energy of an electron in the 3rd excited state?
(ii) If the electron jumps to the ground state from the 3rd excited state, calculate the wavelength of the photon emitted.

Some More Questions From Wave Optics Chapter

Answer the following questions, which help you understand the difference between Thomson's model and Rutherford's model better.
In which model is it completely wrong to ignore multiple scattering for the calculation of average angle of scattering of α-particles by a thin foil?

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Wave Optics

The ground state energy of hydrogen atom is - 13.6 eV.(i) What is the potential energy of an electron in the 3rd excited state?(ii) If the electron jumps to the ground state from the 3rd excited state, calculate the wavelength of the photon emitted.

Some More Questions From Wave Optics Chapter

Answer the following questions, which help you understand the difference between Thomson's model and Rutherford's model better.In which model is it completely wrong to ignore multiple scattering for the calculation of average angle of scattering of α-particles by a thin foil?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

The ground state energy of hydrogen atom is - 13.6 eV.
(i) What is the potential energy of an electron in the 3rd excited state?
(ii) If the electron jumps to the ground state from the 3rd excited state, calculate the wavelength of the photon emitted.

Answer the following questions, which help you understand the difference between Thomson's model and Rutherford's model better.
In which model is it completely wrong to ignore multiple scattering for the calculation of average angle of scattering of α-particles by a thin foil?