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When an electron makes a transition from the n = 3 to the

Chapter 9, Problem 103P

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QUESTION:

When an electron makes a transition from the n = 3 to the n = 2 hydrogen atom Bohr orbit, the energy difference between these two orbits \(\left(3.0 \times 10^{-19} \mathrm{~J}\right)\) is emitted as a photon of light. The relationship between the energy of a photon and its wavelength is given by \(E=h c / \lambda\), where E is the energy of the photon in J, h is Planck’s constant \(\left(6.626 \times 10^{-34} J \cdot s\right)\), and c is the speed of light \(\left(3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}\right)\). Find the wavelength of light emitted by hydrogen atoms when an electron makes this transition.

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QUESTION:

When an electron makes a transition from the n = 3 to the n = 2 hydrogen atom Bohr orbit, the energy difference between these two orbits \(\left(3.0 \times 10^{-19} \mathrm{~J}\right)\) is emitted as a photon of light. The relationship between the energy of a photon and its wavelength is given by \(E=h c / \lambda\), where E is the energy of the photon in J, h is Planck’s constant \(\left(6.626 \times 10^{-34} J \cdot s\right)\), and c is the speed of light \(\left(3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}\right)\). Find the wavelength of light emitted by hydrogen atoms when an electron makes this transition.

ANSWER:

Solution 103P

Given :

Electron makes a transition from the n = 3 to the n = 2 hydrogen atom Bohr orbit.

The energy differ­ence between these two orbits emitted as a photon of light=  (3.0 × 1019 J).

The relationship between the energy of a photon and its wavelength is given by :

 E = ,

where, E = energy of the photon in J,

h = Planck's constant = 6.626 × 10−34

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