The rate constant in s − 1 for a radioactive nuclide that has a half-life of 3.00 hours needs to be calculated. Concept Introduction: The time taken for the reactant’s concentration to reduce to one half of its initial value is called half-life of a reaction.

Question

Clouds of hot, luminous interstellar hydrogen gas can be seen in some parts of the galaxy. In some hydrogen atoms, electrons are excited to quantum levels with n = 100 or higher. (a) Calculate the wavelength observed on Earth if the electrons fall from the level with n = 100 to one with n = 2. (b) In what series would this transition be found? (c) Some of these high-energy electrons fall into intermediate states, such as n = 90. Would the wavelengths of a transition from the state with n = 100 to one with n = 90 be longer or shorter than those in the Balmer series? Explain your answer.

Answer 1

Question

Chapter 20, Problem 72AE

(a)

Interpretation Introduction

Interpretation: The rate constant in s−1 for a radioactive nuclide that has a half-life of 3.00 hours needs to be calculated.

Concept Introduction: The time taken for the reactant’s concentration to reduce to one half of its initial value is called half-life of a reaction.

(b)

Interpretation Introduction

Interpretation: The decay rate in decayss for 1.000 mole of a radioactive nuclide that has a half-life of 3.00 hours needs to be calculated.

Concept Introduction: The time taken for the reactant’s concentration to reduce to one half of its initial value is called half-life of a reaction.

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Clouds of hot, luminous interstellar hydrogen gas can be seen in some parts of the galaxy. In some hydrogen atoms, electrons are excited to quantum levels with n = 100 or higher. (a) Calculate the wavelength observed on Earth if the electrons fall from the level with n = 100 to one with n = 2. (b) In what series would this transition be found? (c) Some of these high-energy electrons fall into intermediate states, such as n = 90. Would the wavelengths of a transition from the state with n = 100 to one with n = 90 be longer or shorter than those in the Balmer series? Explain your answer.

In the spectroscopic technique known as photoelectron spectroscopy (PES), ultraviolet radiation is directed at an atom or molecule. Electrons are ejected from the valence shell and their kinetic energies are measured. Since the energy of the incident ultraviolet photons is known and the kinetic energy of the ejected electron is measured, the ionization energy, I, can be deduced because total energy is conserved. (a) Show that the velocity, v, of the ejected electron and the frequency, n, of the incident radiation are related by hv = I + (1/2)mv^2? (b) Use this relation to calculate the ionization energy of a rubidium atom, knowing that light of wavelength 58.4 nm produces electrons with a velocity of 2,450 km/s Recall that 1 J = 1 kg.m^2/s^2

I) In Millikan's experiment, each droplet observed by the technicians contained an even number of electrons. If they had been unaware of this limitation, how would it have affected their report of an electron's charge?II) Millikan measured the charge of an electron in electrostatic units, esu. The data he collected included the following series of charges found on oil drops: 9.60 X 10^-10 esu, 1.92 X 10^-9 esu; 2.40 X 10^-9 esu; 2.88 X 10^-9 esu; and 4.80 X 10^-9 esu. (a) From this series, find the probable charge of the electron in electrostatic units. (b) Estimate the number of electrons in an oil drop with a charge of 6.72 X 10^-9 esu. The actual charge (in Coulombs) of an electron is 1.602 X 10^-19 C. What is the relationship between esu and Coulombs?

Answer 2

Question

Chapter 20, Problem 72AE

(a)

Interpretation Introduction

Interpretation: The rate constant in s−1 for a radioactive nuclide that has a half-life of 3.00 hours needs to be calculated.

Concept Introduction: The time taken for the reactant’s concentration to reduce to one half of its initial value is called half-life of a reaction.

(b)

Interpretation Introduction

Interpretation: The decay rate in decayss for 1.000 mole of a radioactive nuclide that has a half-life of 3.00 hours needs to be calculated.

Concept Introduction: The time taken for the reactant’s concentration to reduce to one half of its initial value is called half-life of a reaction.

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Answer 3

Question

Chapter 20, Problem 72AE

(a)

Interpretation Introduction

Interpretation: The rate constant in s−1 for a radioactive nuclide that has a half-life of 3.00 hours needs to be calculated.

Concept Introduction: The time taken for the reactant’s concentration to reduce to one half of its initial value is called half-life of a reaction.

(b)

Interpretation Introduction

Interpretation: The decay rate in decayss for 1.000 mole of a radioactive nuclide that has a half-life of 3.00 hours needs to be calculated.

Concept Introduction: The time taken for the reactant’s concentration to reduce to one half of its initial value is called half-life of a reaction.

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Answer 4

Question

Chapter 20, Problem 72AE

(a)

Interpretation Introduction

Interpretation: The rate constant in s−1 for a radioactive nuclide that has a half-life of 3.00 hours needs to be calculated.

Concept Introduction: The time taken for the reactant’s concentration to reduce to one half of its initial value is called half-life of a reaction.

(b)

Interpretation Introduction

Interpretation: The decay rate in decayss for 1.000 mole of a radioactive nuclide that has a half-life of 3.00 hours needs to be calculated.

Concept Introduction: The time taken for the reactant’s concentration to reduce to one half of its initial value is called half-life of a reaction.

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Answer 5

Chapter 20, Problem 72AE

(a)

Interpretation Introduction

Interpretation: The rate constant in s−1 for a radioactive nuclide that has a half-life of 3.00 hours needs to be calculated.

Concept Introduction: The time taken for the reactant’s concentration to reduce to one half of its initial value is called half-life of a reaction.

(b)

Interpretation Introduction

Interpretation: The decay rate in decayss for 1.000 mole of a radioactive nuclide that has a half-life of 3.00 hours needs to be calculated.

Concept Introduction: The time taken for the reactant’s concentration to reduce to one half of its initial value is called half-life of a reaction.

Answer 6

Chapter 20, Problem 72AE

(a)

Interpretation Introduction

Interpretation: The rate constant in s−1 for a radioactive nuclide that has a half-life of 3.00 hours needs to be calculated.

Concept Introduction: The time taken for the reactant’s concentration to reduce to one half of its initial value is called half-life of a reaction.

Answer 7

Chapter 20, Problem 72AE

(a)

Interpretation Introduction

Interpretation: The rate constant in s−1 for a radioactive nuclide that has a half-life of 3.00 hours needs to be calculated.

Concept Introduction: The time taken for the reactant’s concentration to reduce to one half of its initial value is called half-life of a reaction.

Answer 8

(b)

Interpretation Introduction

Interpretation: The decay rate in decayss for 1.000 mole of a radioactive nuclide that has a half-life of 3.00 hours needs to be calculated.

Concept Introduction: The time taken for the reactant’s concentration to reduce to one half of its initial value is called half-life of a reaction.

Answer 9

(b)

Interpretation Introduction

Interpretation: The decay rate in decayss for 1.000 mole of a radioactive nuclide that has a half-life of 3.00 hours needs to be calculated.

Concept Introduction: The time taken for the reactant’s concentration to reduce to one half of its initial value is called half-life of a reaction.

Answer 10

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Answer 21

Ch. 20 - Prob. 1E Ch. 20 - Prob. 2E Ch. 20 - Prob. 3E Ch. 20 - Prob. 4E Ch. 20 - Prob. 5E Ch. 20 - Prob. 6E Ch. 20 - Prob. 7E Ch. 20 - Prob. 8E Ch. 20 - Prob. 9E Ch. 20 - Prob. 10E

The rate constant in s − 1 for a radioactive nuclide that has a half-life of 3.00 hours needs to be calculated. Concept Introduction: The time taken for the reactant’s concentration to reduce to one half of its initial value is called half-life of a reaction.

Solution Summary: The author explains how the decay rate in s-1 is calculated for a radioactive nuclide whose half-life is 3.00 hours.

Concept explainers

Interpretation: The rate constant in s−1 for a radioactive nuclide that has a half-life of 3.00 hours needs to be calculated.

Concept Introduction: The time taken for the reactant’s concentration to reduce to one half of its initial value is called half-life of a reaction.

Interpretation: The decay rate in decayss for 1.000 mole of a radioactive nuclide that has a half-life of 3.00 hours needs to be calculated.

Concept Introduction: The time taken for the reactant’s concentration to reduce to one half of its initial value is called half-life of a reaction.

Chapter 20 Solutions

The rate constant in s − 1 for a radioactive nuclide that has a half-life of 3.00 hours needs to be calculated. Concept Introduction: The time taken for the reactant’s concentration to reduce to one half of its initial value is called half-life of a reaction.

Solution Summary: The author explains how the decay rate in s-1 is calculated for a radioactive nuclide whose half-life is 3.00 hours.

Concept explainers

Interpretation: The rate constant in s−1 for a radioactive nuclide that has a half-life of 3.00 hours needs to be calculated. Concept Introduction: The time taken for the reactant’s concentration to reduce to one half of its initial value is called half-life of a reaction.

Interpretation: The decay rate in decayss for 1.000 mole of a radioactive nuclide that has a half-life of 3.00 hours needs to be calculated. Concept Introduction: The time taken for the reactant’s concentration to reduce to one half of its initial value is called half-life of a reaction.

Chapter 20 Solutions

Interpretation: The rate constant in s−1 for a radioactive nuclide that has a half-life of 3.00 hours needs to be calculated.

Concept Introduction: The time taken for the reactant’s concentration to reduce to one half of its initial value is called half-life of a reaction.

Interpretation: The decay rate in decayss for 1.000 mole of a radioactive nuclide that has a half-life of 3.00 hours needs to be calculated.

Concept Introduction: The time taken for the reactant’s concentration to reduce to one half of its initial value is called half-life of a reaction.