Question 1

In an electron microscope, electrons are accelerated to great velocities. Calculate the wavelength of an electron traveling with a velocity of 7.0 * 10³ kilometers per second. The mass of an electron is 9.1 * 10^-28 g.

Accepted Answer

The wavelength of an electron can be calculated using the de Broglie equation:

wavelength = h/mv where h is Planck's constant, m is the mass of the electron, and v is the velocity of the electron.

Plugging in the given values, we get:

wavelength = (6.626 x 10^-34 J s)/(9.1 x 10^-28 kg)(7.0 x 10^6 m/s)

Simplifying, we get:

wavelength = 1.0 x 10^-10 m or 1.0 angstrom

Therefore, the best choice is D, which is 1.0 x 10^-10 m.

Question 2

"No two electrons in an atom can have the same four quantum numbers" is a statement of

Accepted Answer

This statement is known as the Pauli exclusion principle, which states that no two electrons in an atom can have the same set of four quantum numbers (n, l, ml, ms).

Question 3

Electrons can be used to probe the arrangement of atoms on a solid surface if the wavelength of the electrons is comparable with the spacing between the atoms. Which of the following electron velocities would be appropriate for use in this application if the atoms are separated by 0.320 nm?

Accepted Answer

The de Broglie wavelength of an electron is given by λ = h/p, where h is the Planck's constant and p is the momentum of the electron. For the electrons to probe the arrangement of atoms on a solid surface, their wavelength should be comparable to the spacing between the atoms, i.e., λ ≈ 0.320 nm. Equating this with the de Broglie wavelength equation, we get p = h/λ. Now, the kinetic energy of the electron is given by K = p^2/2m, where m is the mass of the electron. Substituting the values, we get K = (h^2/2mλ^2). Taking the square root of K/m, we get the velocity. Substituting h, m, and λ, we get:

v = (2K/m)^0.5 = [(2*(6.626 x 10^-34 J s)^2)/(9.109 x 10^-31 kg*(0.320 x 10^-9 m)^2)]^0.5 = 2.27 x 10^6 m/s

Therefore, choice A) is the best choice as it corresponds to the appropriate velocity of electrons for probing the arrangement of atoms on a solid surface where the atoms are separated by 0.320 nm.

Question 4

A single pulse of a laser yields an average of 5.00 * 10¹⁸ photons with $\lambda$ = 633 nm. If melting ice to water at 0°C requires 6.01 kJ/mol, what is the fewest number of laser pulses need to melt 10.0 g of ice?

Accepted Answer

The answer of A single pulse of a laser yields...

Question 5

A possible set of quantum numbers for the last electron added to complete an atom of germanium (Ge)in its ground state is

Accepted Answer

The answer of A possible set of quantum numbers for...

Question 6

The maximum number of electrons that can occupy an energy level described by the principal quantum number, n, is

Accepted Answer

The answer of The maximum number of electrons that can...

Question 7

Electrons in an orbital with l = 3 are in a/an

Accepted Answer

The letter designation of an orbital corresponds to the value of the angular momentum quantum number, l. For l = 3, the orbital designation would be f, making choice B the correct answer.

Question 8

When photons with a wavelength of 310. nm strike a magnesium plate, the maximum velocity of the ejected electrons is 3.45 *10⁵ m/s. Calculate the binding energy of electrons to the magnesium surface.

Accepted Answer

The answer of When photons with a wavelength of 310....

Question 9

Calculate the wavelength of a neutron that has a velocity of 250 cm/s. (The mass of a neutron = 1.675 * 10^-24 g; h = 6.626 * 10^-34 J.s)

Accepted Answer

The answer of Calculate the wavelength of a neutron that...

Question 10

Which one of the following sets of quantum numbers is not possible?

Accepted Answer

The answer of Which one of the following sets of...

Question 11

Which one of the following sets of quantum numbers is not possible?

Accepted Answer

The answer of Which one of the following sets of...

Question 12

A common way of initiating certain chemical reactions with light involves the generation of free halogen atoms in solution. If $\Delta$H for the reaction Cl₂(g)$\rarr$ 2Cl(g)is 242.8 kJ/mol, what is the longest wavelength of light that will produce free chlorine atoms in solution?

Accepted Answer

The answer of A common way of initiating certain chemical...

Question 13

A possible set of quantum numbers for the last electron added to complete an atom of gallium (Ga)in its ground state is

Accepted Answer

The last electron added to complete an atom of Ga is the 31st electron. To determine the possible set of quantum numbers for this electron, we can use the Aufbau principle and fill the orbitals in increasing order of energy.

1s2, 2s2, 2p6, 3s2, 3p6, 4s2, 3d10, 4p1

The last electron added is in the 4p orbital. Therefore, the values of n, l, and ml for this electron are 4, 1, and either -1, 0, or 1, respectively. The value of ms (the spin quantum number) is either +1/2 or -1/2.

Looking at the answer choices, only option C has the correct values for n, l, ml, and ms. The other options either have incorrect values or are missing information.

Question 14

The longest wavelength of light that causes electrons to be ejected from the surface of a copper plate is 243 nm. What is the maximum velocity of the electrons ejected when light of wavelength 200. nm shines on a copper plate?

Accepted Answer

We can use the formula for the maximum kinetic energy of an ejected electron:

$K_{max} = h
u - W$

where $h$ is Planck's constant, $
u$ is the frequency of the incident light, and $W$ is the work function (energy required to remove an electron) of the metal. We can also use the fact that $c = \lambda 
u$, where $c$ is the speed of light, and $\lambda$ is the wavelength.

Since the longest wavelength that causes ejection is 243 nm, we can find the work function:

$W = h
u_{max} = hc/\lambda_{max} = (6.626 	imes 10^{-34} J\cdot s)(3.00 	imes 10^8 m/s)/(243 	imes 10^{-9} m) = 8.15 	imes 10^{-19} J$

Now we can find the maximum velocity of the ejected electron for light of wavelength 200 nm:

$
u = c/\lambda = (3.00 	imes 10^8 m/s)/(200 	imes 10^{-9} m) = 1.50 	imes 10^{15} Hz$

$K_{max} = h
u - W = (6.626 	imes 10^{-34} J\cdot s)(1.50 	imes 10^{15} Hz) - (8.15 	imes 10^{-19} J) = 9.91 	imes 10^{-19} J$

$K_{max}$ is also equal to the kinetic energy of the ejected electron:

$K_{max} = (1/2)mv^2$

where $m$ is the mass of the electron and $v$ is its velocity. Solving for $v$:

$v = \sqrt{(2K_{max})/m} = \sqrt{(2 	imes 9.91 	imes 10^{-19} J)/(9.11 	imes 10^{-31} kg)} = 6.22 	imes 10^{5} m/s = 6.22 	imes 10^{14} nm/s$

Therefore, the maximum velocity of the electrons ejected by light of wavelength 200 nm is 6.22 x 10^14 nm/s, or approximately 6.22 x 10^5 m/s, which corresponds to answer choice B.

Question 15

If a hydrogen atom and a helium atom have the same kinetic energy,

Accepted Answer

According to the de Broglie wavelength equation, the wavelength (λ) is inversely proportional to the square root of the mass (m) of the particle and directly proportional to the square root of its kinetic energy (K). So, for particles with the same kinetic energy, the one with lower mass will have a longer wavelength. Since the mass of helium is about 4 times higher than the mass of hydrogen, the wavelength of the hydrogen atom will be about 2 times longer than the wavelength of the helium atom.

Question 16

Calculate the wavelength associated with a ²⁰Ne⁺ ion moving at a velocity of 2.0 * 10⁵ m/s. The atomic mass of Ne-20 is 19.992 amu.

Accepted Answer

The answer of Calculate the wavelength associated with a ²⁰Ne⁺...

Question 17

How many orbitals are allowed in a subshell if the angular momentum quantum number for electrons in that subshell is 3?

Accepted Answer

The answer of How many orbitals are allowed in a...

Question 18

The orbital diagram for a ground-state nitrogen atom is

Accepted Answer

The answer of The orbital diagram for a ground-state nitrogen...

Question 19

What is the maximum number of electrons in an atom that can have the following set of quantum numbers? n = 4 l = 3 m_l = -2 m_s = +1/2

Accepted Answer

The answer of What is the maximum number of electrons...

Question 20

The number of orbitals in a d subshell is

Accepted Answer

The number of orbitals in a d subshell is given by 2l+1, where l is the angular momentum quantum number. For d subshell, l=2, so the number of orbitals is 2(2)+1=5. Therefore, the correct answer is D, with 5 as the number of orbitals in a d subshell.

Quiz 7: The Electronic Structure of Atoms

In an electron microscope, electrons are accelerated to great velocities. Calculate the wavelength of an electron traveling with a velocity of 7.0 * 10³ kilometers per second. The mass of an electron is 9.1 * 10^-28 g.

"No two electrons in an atom can have the same four quantum numbers" is a statement of

Electrons can be used to probe the arrangement of atoms on a solid surface if the wavelength of the electrons is comparable with the spacing between the atoms. Which of the following electron velocities would be appropriate for use in this application if the atoms are separated by 0.320 nm?

A single pulse of a laser yields an average of 5.00 * 10¹⁸ photons with $\lambda$ = 633 nm. If melting ice to water at 0°C requires 6.01 kJ/mol, what is the fewest number of laser pulses need to melt 10.0 g of ice?

A possible set of quantum numbers for the last electron added to complete an atom of germanium (Ge) in its ground state is

The maximum number of electrons that can occupy an energy level described by the principal quantum number, n, is

Electrons in an orbital with l = 3 are in a/an

When photons with a wavelength of 310. nm strike a magnesium plate, the maximum velocity of the ejected electrons is 3.45 *10⁵ m/s. Calculate the binding energy of electrons to the magnesium surface.

Calculate the wavelength of a neutron that has a velocity of 250 cm/s. (The mass of a neutron = 1.675 * 10^-24 g; h = 6.626 * 10^-34 J.s)

Which one of the following sets of quantum numbers is not possible?

Which one of the following sets of quantum numbers is not possible?

A common way of initiating certain chemical reactions with light involves the generation of free halogen atoms in solution. If $\Delta$ H for the reaction Cl₂(g) $\rarr$ 2Cl(g) is 242.8 kJ/mol, what is the longest wavelength of light that will produce free chlorine atoms in solution?

A possible set of quantum numbers for the last electron added to complete an atom of gallium (Ga) in its ground state is

The longest wavelength of light that causes electrons to be ejected from the surface of a copper plate is 243 nm. What is the maximum velocity of the electrons ejected when light of wavelength 200. nm shines on a copper plate?

If a hydrogen atom and a helium atom have the same kinetic energy,

Calculate the wavelength associated with a ²⁰Ne⁺ ion moving at a velocity of 2.0 * 10⁵ m/s. The atomic mass of Ne-20 is 19.992 amu.

How many orbitals are allowed in a subshell if the angular momentum quantum number for electrons in that subshell is 3?

The orbital diagram for a ground-state nitrogen atom is

What is the maximum number of electrons in an atom that can have the following set of quantum numbers? n = 4 l = 3 m_l = -2 m_s = +1/2

The number of orbitals in a d subshell is

Quiz 7: The Electronic Structure of Atoms

In an electron microscope, electrons are accelerated to great velocities. Calculate the wavelength of an electron traveling with a velocity of 7.0 * 103 kilometers per second. The mass of an electron is 9.1 * 10-28 g.

"No two electrons in an atom can have the same four quantum numbers" is a statement of

Electrons can be used to probe the arrangement of atoms on a solid surface if the wavelength of the electrons is comparable with the spacing between the atoms. Which of the following electron velocities would be appropriate for use in this application if the atoms are separated by 0.320 nm?

A single pulse of a laser yields an average of 5.00 * 1018 photons with λ\lambdaλ = 633 nm. If melting ice to water at 0°C requires 6.01 kJ/mol, what is the fewest number of laser pulses need to melt 10.0 g of ice?

A possible set of quantum numbers for the last electron added to complete an atom of germanium (Ge) in its ground state is

The maximum number of electrons that can occupy an energy level described by the principal quantum number, n, is

Electrons in an orbital with l = 3 are in a/an

When photons with a wavelength of 310. nm strike a magnesium plate, the maximum velocity of the ejected electrons is 3.45 *105 m/s. Calculate the binding energy of electrons to the magnesium surface.

Calculate the wavelength of a neutron that has a velocity of 250 cm/s. (The mass of a neutron = 1.675 * 10-24 g; h = 6.626 * 10-34 J.s)

Which one of the following sets of quantum numbers is not possible?

Which one of the following sets of quantum numbers is not possible?

A common way of initiating certain chemical reactions with light involves the generation of free halogen atoms in solution. If Δ\DeltaΔ H for the reaction Cl2(g) →\rarr→ 2Cl(g) is 242.8 kJ/mol, what is the longest wavelength of light that will produce free chlorine atoms in solution?

A possible set of quantum numbers for the last electron added to complete an atom of gallium (Ga) in its ground state is

The longest wavelength of light that causes electrons to be ejected from the surface of a copper plate is 243 nm. What is the maximum velocity of the electrons ejected when light of wavelength 200. nm shines on a copper plate?

If a hydrogen atom and a helium atom have the same kinetic energy,

Calculate the wavelength associated with a 20Ne+ ion moving at a velocity of 2.0 * 105 m/s. The atomic mass of Ne-20 is 19.992 amu.

How many orbitals are allowed in a subshell if the angular momentum quantum number for electrons in that subshell is 3?

The orbital diagram for a ground-state nitrogen atom is

What is the maximum number of electrons in an atom that can have the following set of quantum numbers? n = 4 l = 3 ml = -2 ms = +1/2

The number of orbitals in a d subshell is

In an electron microscope, electrons are accelerated to great velocities. Calculate the wavelength of an electron traveling with a velocity of 7.0 * 10³ kilometers per second. The mass of an electron is 9.1 * 10^-28 g.

A single pulse of a laser yields an average of 5.00 * 10¹⁸ photons with $\lambda$ = 633 nm. If melting ice to water at 0°C requires 6.01 kJ/mol, what is the fewest number of laser pulses need to melt 10.0 g of ice?

When photons with a wavelength of 310. nm strike a magnesium plate, the maximum velocity of the ejected electrons is 3.45 *10⁵ m/s. Calculate the binding energy of electrons to the magnesium surface.

Calculate the wavelength of a neutron that has a velocity of 250 cm/s. (The mass of a neutron = 1.675 * 10^-24 g; h = 6.626 * 10^-34 J.s)

A common way of initiating certain chemical reactions with light involves the generation of free halogen atoms in solution. If $\Delta$ H for the reaction Cl₂(g) $\rarr$ 2Cl(g) is 242.8 kJ/mol, what is the longest wavelength of light that will produce free chlorine atoms in solution?

Calculate the wavelength associated with a ²⁰Ne⁺ ion moving at a velocity of 2.0 * 10⁵ m/s. The atomic mass of Ne-20 is 19.992 amu.

What is the maximum number of electrons in an atom that can have the following set of quantum numbers? n = 4 l = 3 m_l = -2 m_s = +1/2