A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of photon.

Solution

Initially, hydrogen is in the ground state.
After absorption of photon Hydrogen atom excited to level, n=4.

Energy of an electron in n^th orbit of H atom is,

E_{n} = \frac{- 13.6}{n^{2}} eV w h e n n = 1; E_{1} = - 13.6 eV

Energy in

4^{th}

(n = 4) level

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

∴

∆ E = E_{4} - E_{1}

∆ E = - 0.85 - (- 13.6) eV = - 0.85 + 13.6 \Rightarrow ∆ E = 12.75 eV N o w, e n e r g y o f a p h o t o n = h ν T h e r e f o r e, hv = 12.75 eV \Rightarrow hv = 12.75 \times 1.6 \times 10^{- 19} J \Rightarrow v = \frac{12.75 \times 1.6 \times 10^{- 19}}{6.6 \times 10^{- 34}} i . e ., v = 3.078 \times 10^{15} Hz, i s t h e r e q u i r e d f r e q u e n c y o f t h e p h o t o n . N o w, w a v e l e n g t h o f p h o t o n i s, λ = \frac{c}{λ} = \frac{3 \times 10^{8}}{3.078 \times 10^{15}} i . e ., λ = 974.4 Å

Some More Questions From Wave Optics Chapter

The size of the atom in Thomson's model is _________ the atomic size in Rutherford's model. (much greater than/no different from/much less than)

In the ground state of electrons are in stable equilibrium, while in electrons always experience a net force. (Thomson's model/Rutherford's model).

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Wave Optics

A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of photon.

Some More Questions From Wave Optics Chapter

The size of the atom in Thomson's model is _________ the atomic size in Rutherford's model. (much greater than/no different from/much less than)

In the ground state of electrons are in stable equilibrium, while in electrons always experience a net force. (Thomson's model/Rutherford's model).

A classical atom based on __________ is doomed to collapse. (Thomson's model/Rutherford's model)

An atom has a nearly continuous mass distribution in a ___ but has a highly non-uniform mass distribution in (Thomson's model/Rutherford's model)

The positively charged part of the atom possesses most of the mass in ___________ (Rutherford's model/both the models).

Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil. (Hydrogen is a solid at temperatures below 14 K.) What results do you expect?

Mock Test Series

NCERT Sample Papers

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For Daily Free Study Material Join wiredfaculty

Wave Optics

A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of photon.

Some More Questions From Wave Optics Chapter

The size of the atom in Thomson's model is _________ the atomic size in Rutherford's model. (much greater than/no different from/much less than)

In the ground state of __________ electrons are in stable equilibrium, while in __________ electrons always experience a net force. (Thomson's model/Rutherford's model).

A classical atom based on __________ is doomed to collapse. (Thomson's model/Rutherford's model)

An atom has a nearly continuous mass distribution in a _____________ but has a highly non-uniform mass distribution in __________ (Thomson's model/Rutherford's model)

The positively charged part of the atom possesses most of the mass in ___________ (Rutherford's model/both the models).

Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil. (Hydrogen is a solid at temperatures below 14 K.) What results do you expect?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

In the ground state of electrons are in stable equilibrium, while in electrons always experience a net force. (Thomson's model/Rutherford's model).

An atom has a nearly continuous mass distribution in a ___ but has a highly non-uniform mass distribution in (Thomson's model/Rutherford's model)