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Why is a metastable state necessary for the production of laser light?

Laser light relies on the process of stimulated emission. In this process, electrons must be prepared in an excited (upper) metastable state such that the passage of light through the system produces de-excitations and, therefore, additional light.

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How does light from an incandescent light bulb differ from laser light?

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How is a Blu-Ray player able to read more information that a CD player?

A Blu-Ray player uses blue laser light to probe the bumps and pits of the disc and a CD player uses red laser light. The relatively short-wavelength blue light is necessary to probe the smaller pits and bumps on a Blu-ray disc; smaller pits and bumps correspond to higher storage densities.

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What are the similarities and differences between a CD player and a Blu-Ray player?

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Problems

A carbon dioxide laser used in surgery emits infrared radiation with a wavelength of 10.6 μ m . In 1.00 ms, this laser raised the temperature of 1.00 cm 3 of flesh to 100 °C and evaporated it. (a) How many photons were required? You may assume that flesh has the same heat of vaporization as water. (b) What was the minimum power output during the flash?

a. If flesh has the same density as water, then we used 1.34 × 10 23 photons. b. 2.52 MW

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An excimer laser used for vision correction emits UV radiation with a wavelength of 193 nm. (a) Calculate the photon energy in eV. (b) These photons are used to evaporate corneal tissue, which is very similar to water in its properties. Calculate the amount of energy needed per molecule of water to make the phase change from liquid to gas. That is, divide the heat of vaporization in kJ/kg by the number of water molecules in a kilogram. (c) Convert this to eV and compare to the photon energy. Discuss the implications.

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Additional problems

For a hydrogen atom in an excited state with principal quantum number n , show that the smallest angle that the orbital angular momentum vector can make with respect to the z -axis is θ = cos −1 ( n 1 n ) .

The smallest angle corresponds to l = n 1 and m = l = n 1 . Therefore θ = cos −1 ( n 1 n ) .

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What is the probability that the 1 s electron of a hydrogen atom is found between r = 0 and r = ?

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Sketch the potential energy function of an electron in a hydrogen atom. (a) What is the value of this function at r = 0 ? in the limit that r = ? (b) What is unreasonable or inconsistent with the former result?

a. According to [link] , when r = 0 , U ( r ) = , and when r = + , U ( r ) = 0 . b. The former result suggests that the electron can have an infinite negative potential energy. The quantum model of the hydrogen atom avoids this possibility because the probability density at r = 0 is zero.

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Find the value of l , the orbital angular momentum quantum number, for the Moon around Earth.

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Show that the maximum number of orbital angular momentum electron states in the n th shell of an atom is n 2 . (Ignore electron spin.) ( Hint: Make a table of the total number of orbital angular momentum states for each shell and find the pattern.)

A formal solution using sums is somewhat complicated. However, the answer easily found by studying the mathematical pattern between the principal quantum number and the total number of orbital angular momentum states.
For n = 1 , the total number of orbital angular momentum states is 1; for n = 2 , the total number is 4; and, when n = 3 , the total number is 9, and so on. The pattern suggests the total number of orbital angular momentum states for the n th shell is n 2 .
(Later, when we consider electron spin, the total number of angular momentum states will be found to be 2 n 2 , because each orbital angular momentum states is associated with two states of electron spin; spin up and spin down).

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What is the magnitude of an electron magnetic moment?

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What is the maximum number of electron states in the n = 5 shell?

50

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A ground-state hydrogen atom is placed in a uniform magnetic field, and a photon is emitted in the transition from a spin-up to spin-down state. The wavelength of the photon is 168 μ m . What is the strength of the magnetic field?

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Show that the maximum number of electron states in the n th shell of an atom is 2 n 2 .

The maximum number of orbital angular momentum electron states in the n th shell of an atom is n 2 . Each of these states can be filled by a spin up and spin down electron. So, the maximum number of electron states in the n th shell is 2 n 2 .

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The valence electron of chlorine is excited to a 3 p state. (a) What is the magnitude of the electron’s orbital angular momentum? (b) What are possible values for the z -component of angular measurement?

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Which of the following notations are allowed (that is, which violate none of the rules regarding values of quantum numbers)? (a) 1 s 1 ; (b) 1 d 3 ; (c) 4 s 2 ; (d) 3 p 7 ; (e) 6 h 20

a., c., and e. are allowed; the others are not allowed. b. l > n is not allowed.
d. 7 > 2 ( 2 l + 1 )

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The ion Be 3+ makes an atomic transition from an n = 3 state to an n = 2 state. (a) What is the energy of the photon emitted during the transition? (b) What is the wavelength of the photon?

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The maximum characteristic X-ray photon energy comes from the capture of a free electron into a K shell vacancy. What is this photon frequency for tungsten, assuming that the free electron has no initial kinetic energy?

f = 1.8 × 10 9 Hz

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Derive an expression for the ratio of X-ray photon frequency for two elements with atomic numbers Z 1 and Z 2 .

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Compare the X-ray photon wavelengths for copper and silver.

The atomic numbers for Cu and Ag are Z = 29 and 47, respectively. The X-ray photon frequency for silver is greater than copper by the following factor:
( f Ag f Cu ) 2 = 2.7 .
Therefore, the X-ray wavelength of Ag is about three times shorter than for copper.

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(a) What voltage must be applied to an X-ray tube to obtain 0.0100-fm-wavelength X-rays for use in exploring the details of nuclei? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

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A student in a physics laboratory observes a hydrogen spectrum with a diffraction grating for the purpose of measuring the wavelengths of the emitted radiation. In the spectrum, she observes a yellow line and finds its wavelength to be 589 nm. (a) Assuming that this is part of the Balmer series, determine n i , the principal quantum number of the initial state. (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

a. 3.24; b. n i is not an integer. c. The wavelength must not be correct. Because n i > 2 , the assumption that the line was from the Balmer series is possible, but the wavelength of the light did not produce an integer value for n i . If the wavelength is correct, then the assumption that the gas is hydrogen is not correct; it might be sodium instead.

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Practice Key Terms 6

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Source:  OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4
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