Chapter 11, Problem 91E

Interpretation Introduction

(a)

Interpretation:

The difference between continuous spectrum and discrete line spectrum in scientific terms is to be stated.

Concept introduction:

Each element produces a unique spectrum that is used to identify the elements. There are many possible transitions of electrons in principal energy level. Some of them are more probable and some are less probable. Some are present in visible spectral range, some are present out of visible spectral range.

Answer to Problem 91E

A continuous spectrum gives continuous change in colors while discrete line spectrum gives discrete color lines, which are separated by particular distance.

Explanation of Solution

A spectrum which contains continuous change in colors is called continuous spectrum, it does not contains distinct separation of colors. The distance between two energy states in continuous spectrum is almost equal to zero. This spectrum gives the white light. Discrete line spectrum gives discrete colors line and they are separated by particular distance.

Conclusion

A continuous spectrum gives continuous change in colors while discrete line spectrum gives discrete color lines, which are separated by particular distance.

Interpretation Introduction

(b)

Interpretation:

The difference between quantized and continuous in scientific terms is to be stated.

Concept introduction:

An amount that is limited to specific values and may never be between two of those values, is called quantized. An amount that can have any value between any two values is called continuous. There is an infinite number of other acceptable value.

Answer to Problem 91E

An amount is said to be quantized if it is limited to specific values, while an amount is said to be continuous if it have any value between any two values.

Explanation of Solution

An amount is said to be quantized if it is limited within the range of some given specific values and may never be between two of those values. An amount is said to be continuous if it have any random value between two of those values. A line spectrum is quantized but a spectrum of white light is continuous.

Conclusion

An amount is said to be quantized if it is limited to specific values, while an amount is said to be continuous if it have any value between any two values.

Interpretation Introduction

(c)

Interpretation:

The difference between ground state and excited state in scientific terms is to be stated.

Concept introduction:

The electron is normally found in its ground state. The ground state is the conditions when the electron is in $n=1$ (for a hydrogen atom) or when all electrons in an atom occupy the lowest possible energy levels. If an atom absorbs energy, an electron can be raised to an excited state.

Answer to Problem 91E

Ground state is the lowest possible energy level in which electrons are arranged, while in excited state electrons are not arranged is the lowest possible energy level.

Explanation of Solution

The possible lowest energy level in which electrons are arranged is known as ground state. Initially an electron stayed in its ground state energy level. If an atom absorbs energy, it undergoes excitation and jumps from lower energy level to the higher energy level, which is known as excited state.

Conclusion

Ground state is the lowest possible energy level in which electrons are arranged, while in excited state electrons are not arranged is the lowest possible energy level.

Interpretation Introduction

(d)

Interpretation:

The difference between principal energy level and principal quantum number in scientific terms is to be stated.

Concept introduction:

Niels Bohr made a huge contribution to the development of modern atomic theory. Bohr introduced the idea of quantized electron energy levels in the atom. These levels appear in modern theory as quantum energy levels, which are identified by the principal quantum number, $n$.

Answer to Problem 91E

The principal energy level is identified by the principal quantum number, which represent the energy levels of orbitals.

Explanation of Solution

The principal energy level is identified by the principal quantum number. The principal quantum number represents the energy of orbitals. The first principal energy level is $n=1$, and the second is $n=2$, and so on. There is infinite number of principal energy levels. The relative energy possessed by an electron depends on the principal energy level.

Conclusion

The principal energy level is identified by the principal quantum number, which represent the energy levels of orbitals.

Interpretation Introduction

(e)

Interpretation:

The difference between Bohr model of the atom and quantum mechanical model of the atom is to be stated.

Concept introduction:

Niels Bohr suggested that an atom consists of an extremely dense nucleus. This nucleus contains all of the atom’s positive charge and nearly all of its mass and negatively charged electrons of very small mass travel in orbits around the nucleus. The quantum mechanical model keeps the quantized energy levels that Bohr introduced, which is appeared in the quantum theory as principal energy levels

Answer to Problem 91E

Bohr model successfully described the structure and properties of hydrogen atom, while quantum mechanical model succeed in disrobing hydrogen and multi electron atoms.

Explanation of Solution

Bohr model suggested a reasonable explanation for the atomic line spectra in terms of electron energies. Bohr also introduced the idea of quantized electron energy levels in the atom. These levels appear in modern theory as principal energy levels and these principal energy levels are identified by the principal quantum number, $n$. The quantum mechanical model succeeds in disrobing hydrogen and multi electron atoms.

Conclusion

Bohr model successfully described the structure and properties of hydrogen atom, while quantum mechanical model succeed in disrobing hydrogen and multi electron atoms.

Interpretation Introduction

(f)

Interpretation:

The difference among principal energy level, sublevel, and orbital in scientific terms is to be stated.

Concept introduction:

The number of shells in the atom is equal to the principal energy levels. The region in space where the probability of finding electrons is maximum which is represented by the sublevel. In the sublevel the most probable location of the electrons in three dimensional view is explained by an orbital.

Answer to Problem 91E

The principal energy level represents the energy of orbitals. Sublevel represents the maximum probability of finding electrons within the region. The most probable location of the electrons in three dimensional view is explained by orbital.

Explanation of Solution

The principal energy level is identified by the principal quantum number. The principal quantum number represents the energy of orbitals. Sublevels indicate the energies that are associated with the electrons. There is one sublevel for each principal energy level, which contains one orbital. In the sublevel the most probable location of the electrons in three dimensional view is explained by an orbital.

Conclusion

The principal energy level represents the energy of orbitals. Sublevel represents the maximum probability of finding electrons within the region. The most probable location of the electrons in three dimensional view is explained by orbital.

Interpretation Introduction

(g)

Interpretation:

The difference among the sublevels $s,p,d$, and $f$ in scientific terms is to be stated.

Concept introduction:

The principal energy levels are identified by the principal quantum number, $n$. In quantum mechanical model, for each principal energy level there are one or more sublevels. These sublevels are, $s,p,d,$ and $f$. A specific sublevel is identified by both the principal energy level and sublevel.

Answer to Problem 91E

The energy of each principal energy levels spread over a range related to the sublevels. The energy increase in the order of sublevels $s,p,d$, and $f$, which is shown below.

$s<p<d<f$.

Explanation of Solution

The total number of sublevels or orbitals within a given principal level is equal to the principal quantum number, $n$. For $n=1$, there is one orbital or sublevel indicated as $1s$. For $n=2$, there are two sublevels, indicated as $2s$ and $2p$. For $n=3$, there are three sublevels, $3s,3p,$ and $3d$, and so on. The energy of each principal energy levels spread over a range related to the sublevels. The energy increase in the order of $s,p,d$, and $f$, which is shown below.

$s<p<d<f$.

Conclusion

The energy of each principal energy levels spread over a range related to the sublevels. The energy increase in the order of sublevels $s,p,d$, and $f$, which is shown below.

$s<p<d<f$.

Interpretation Introduction

(h)

Interpretation:

The difference between orbit, and orbitals in scientific terms is to be stated.

Concept introduction:

The three dimensional region in space where the probability of finding electrons is maximum is called an orbital. An orbit is defined as the fixed path around which electrons revolve. An orbital is embedded in an orbit.

Answer to Problem 91E

The three dimensional region in space where the probability of finding electrons is maximum is called an orbital. An orbit is the fixed path around which electrons revolve around the nucleus of atoms.

Explanation of Solution

The region in space around a nucleus in which there is a high probability of finding of electron. The region is called orbitals. An orbit is defined as the fixed circular path of nucleus in which electrons revolve around the nucleus of atoms.

Conclusion

The three dimensional region in space where the probability of finding electrons is maximum is called an orbital. An orbit is the fixed path around which electrons revolve around the nucleus of atoms.

Interpretation Introduction

(i)

Interpretation:

The difference among first, second, third ionization energies in scientific terms is to be stated.

Concept introduction:

The ionization energy is the measurement of energy, which is required to remove an electron from a neutral atom. An atom acquires a positive charge when it removes an electron from its valence shell. The valence shell electron is loosely bind, which is easily removed.

Answer to Problem 91E

The energy required to remove one electron from a neutral gaseous atom of an element is called first ionization energy. The energy required to remove second electron from $+1$ ion of an element is called second ionization energy. Similarly, the energy required to remove third electron from $+2$ ion of an element is called third ionization energy.

Explanation of Solution

The energy required to remove one electron from a neutral gaseous atom of an element is called first ionization energy. The energy required to remove second electron from $+1$ ion of an element is called second ionization energy. Similarly, the energy required to remove third electron from $+2$ ion of an element is called third ionization energy. Thus, the strength of attraction forces between the electrons and the positively charged nucleus increases as compare as neutral atom. Therefore, the second ionization energy of an element is always greater than the first ionization energy and the third ionization energy of an element is always greater than the second ionization energy.

Conclusion

The energy required to remove one electron from a neutral gaseous atom of an element is called first ionization energy. The energy required to remove second electron from $+1$ ion of an element is called second ionization energy. Similarly, the energy required to remove third electron from $+2$ ion of an element is called third ionization energy.

Interpretation Introduction

(j)

Interpretation:

The difference between metal, nonmetal, metalloid, and semimetal in scientific terms is to be stated.

Concept introduction:

Those elements that have tendency to form positive ion by losing electrons are called metals. The elements that have tendency to form anions by gaining electrons are called nonmetal. Metalloids are the elements that have some properties of both metal and nonmetal.

Answer to Problem 91E

Metals are the elements that have tendency to form positive ion by losing electrons and nonmetal are the elements that have tendency to form anions by gaining electrons. Metalloids or semimetals are the elements having the properties of both metal and nonmetal.

Explanation of Solution

A metal hast tendency to form positive ion by losing electrons. Thus, metals are electropositive elements. A nonmetal has tendency to form anions by gaining electrons. Thus, nonmetals are electronegative elements. Most of the elements next to the stair-step line have some properties of metal and nonmetal. These elements are called metalloids or semimetals.

Conclusion

Metals are the elements that have tendency to form positive ion by losing electrons and nonmetal are the elements that have tendency to form anions by gaining electrons. Metalloids or semimetals are the elements that have some properties of both metal and nonmetal.