Physics
Physics
3rd Edition
ISBN: 9780073512150
Author: Alan Giambattista, Betty Richardson, Robert C. Richardson Dr.
Publisher: McGraw-Hill Education
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Question
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Chapter 28, Problem 88P

(a)

To determine

The ionisation energy required to remove an electron from the ground level.

(a)

Expert Solution
Check Mark

Answer to Problem 88P

The ionisation energy is 5.1eV.

Explanation of Solution

The ground state energy of sodium is 5.1 eV.

The ionisation energy is the energy required to move an electron from the given state to the infinite state and is given by the energy difference between the two states.

Write the relation between En and E1 using Bohr model

En=E1n2                                                               (I)

Here E1 is the ground state energy. En is the energy of the nth state and n is the state of the electron.

Write the expression for energy difference between ground state and nth state

ΔE=EnE1                                                         (II)

Here, ΔE is the energy difference, E1 is the ground state energy. En is the energy of the nth state.

Substituting (I) in (II) and substituting 2 for n

ΔE=(1n21)E1                                                          (III)

Substituting for n in (III) to find ΔE and substituting 5.1 eV for E1

ΔE=(121)E1=E1=5.1 eV

Thus, the ionisation energy is 5.1 eV.

(b)

To determine

The wavelength of the emitted radiation during the transition 3d to 3p level.

(b)

Expert Solution
Check Mark

Answer to Problem 88P

The wavelength of the emitted radiation is 890 nm.

Explanation of Solution

The energy of 3d level is 1.6 eV and the energy of 3p level is 3.0 eV.

Write the expression for the wavelength of the emitted radiation due to transition.

λ=hcΔE                                                                    (IV)

Here, λ is the wavelength, h is the Planck’s constant, ΔE is the energy difference and c is the speed of light.

Write the expression for energy difference between 3d and 3p levels

ΔE=E3dE3p                                                               (V)

Here, E3d is the energy of 3d state and E3p is the energy of the 3p state.

Substituting (V) in (IV)

λ=hcE3dE3p                                                                   (VI)

Substituting 1.6 eV for E3d and 3.0 eV for E3p and 1240 eV.nm for hc in (VI) to find λ

λ=1240 eV.nm1.60 eV(3.0 eV)=1240 eV.nm3.0 eV1.60 eV=890 nm

Thus, the wavelength of the emitted radiation is 890 nm.

(c)

To determine

The transition corresponding to characteristic yellow light of sodium.

(c)

Expert Solution
Check Mark

Answer to Problem 88P

The transition 3p3s will emit the characteristic yellow light.

Explanation of Solution

The wavelength of the yellow light is 589nm.

The energy of 3s level is 5.1 eV and the energy of 3p level is 3.0 eV.

Write the expression for energy

E=hcλ                                                                   (VII)

Substituting 1240 eV.nm for hc and  589nm for λ in (VII) to find E

E=1240eV.nm589nm=2.11 eV

Write the expression for energy difference between 3p and 3s level

ΔE=E3pE3s                                                               (VIII)

Here, E3s is the energy of 3s state and E3p is the energy of the 3p state.

Substituting 5.1 eV for E3s and 3.0 eV for E3p in (VIII) to find ΔE

ΔE=3.0 eV(5.1 eV)=2.1 eV

Since E and ΔE are approximately the same, the transition 3p3s will emit the characteristic yellow light.

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Chapter 28 Solutions

Physics

Ch. 28 - Prob. 2CQCh. 28 - Prob. 3CQCh. 28 - Prob. 4CQCh. 28 - Prob. 5CQCh. 28 - Prob. 6CQCh. 28 - Prob. 7CQCh. 28 - Prob. 8CQCh. 28 - Prob. 9CQCh. 28 - Prob. 10CQCh. 28 - Prob. 11CQCh. 28 - Prob. 12CQCh. 28 - Prob. 13CQCh. 28 - Prob. 14CQCh. 28 - Prob. 15CQCh. 28 - Prob. 16CQCh. 28 - Prob. 17CQCh. 28 - Prob. 18CQCh. 28 - Prob. 1MCQCh. 28 - Prob. 2MCQCh. 28 - Prob. 3MCQCh. 28 - Prob. 4MCQCh. 28 - Prob. 5MCQCh. 28 - Prob. 6MCQCh. 28 - Prob. 7MCQCh. 28 - Prob. 8MCQCh. 28 - Prob. 9MCQCh. 28 - Prob. 10MCQCh. 28 - Prob. 1PCh. 28 - Prob. 2PCh. 28 - Prob. 3PCh. 28 - Prob. 4PCh. 28 - Prob. 5PCh. 28 - Prob. 6PCh. 28 - Prob. 7PCh. 28 - Prob. 8PCh. 28 - Prob. 9PCh. 28 - Prob. 10PCh. 28 - Prob. 11PCh. 28 - Prob. 12PCh. 28 - Prob. 13PCh. 28 - Prob. 14PCh. 28 - Prob. 15PCh. 28 - Prob. 16PCh. 28 - Prob. 17PCh. 28 - Prob. 18PCh. 28 - Prob. 19PCh. 28 - Prob. 20PCh. 28 - Prob. 21PCh. 28 - Prob. 22PCh. 28 - Prob. 23PCh. 28 - Prob. 24PCh. 28 - Prob. 25PCh. 28 - Prob. 26PCh. 28 - Prob. 27PCh. 28 - Prob. 28PCh. 28 - Prob. 29PCh. 28 - Prob. 30PCh. 28 - Prob. 31PCh. 28 - Prob. 32PCh. 28 - Prob. 33PCh. 28 - Prob. 34PCh. 28 - Prob. 35PCh. 28 - Prob. 36PCh. 28 - Prob. 37PCh. 28 - Prob. 38PCh. 28 - Prob. 39PCh. 28 - Prob. 40PCh. 28 - Prob. 41PCh. 28 - Prob. 42PCh. 28 - Prob. 43PCh. 28 - Prob. 44PCh. 28 - Prob. 45PCh. 28 - Prob. 46PCh. 28 - Prob. 47PCh. 28 - Prob. 48PCh. 28 - Prob. 49PCh. 28 - Prob. 50PCh. 28 - Prob. 51PCh. 28 - Prob. 52PCh. 28 - Prob. 53PCh. 28 - Prob. 54PCh. 28 - Prob. 55PCh. 28 - Prob. 56PCh. 28 - Prob. 57PCh. 28 - Prob. 58PCh. 28 - Prob. 59PCh. 28 - Prob. 60PCh. 28 - Prob. 61PCh. 28 - Prob. 62PCh. 28 - Prob. 63PCh. 28 - Prob. 64PCh. 28 - Prob. 65PCh. 28 - Prob. 66PCh. 28 - Prob. 67PCh. 28 - Prob. 68PCh. 28 - Prob. 69PCh. 28 - Prob. 70PCh. 28 - Prob. 71PCh. 28 - Prob. 72PCh. 28 - Prob. 73PCh. 28 - Prob. 74PCh. 28 - Prob. 75PCh. 28 - Prob. 76PCh. 28 - Prob. 77PCh. 28 - Prob. 78PCh. 28 - Prob. 79PCh. 28 - Prob. 80PCh. 28 - Prob. 81PCh. 28 - Prob. 82PCh. 28 - Prob. 83PCh. 28 - Prob. 84PCh. 28 - Prob. 85PCh. 28 - Prob. 86PCh. 28 - Prob. 87PCh. 28 - Prob. 88P
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