Question 1

A group of hydrogen-like atoms (atoms with only one electron)are in their ground state.Light of increasing intensity is shone at these atoms until the light becomes absorbed by the atoms.The longest wavelength of light when this occurs is 7.61 nm.What is the ground state energy of these atoms?
A)91.8 eV
B)13.6 eV
C)218 eV
D)122 eV
E)54 eV

Accepted Answer

The answer of A group of hydrogen-like atoms (atoms with...

Question 2

Find the wavelength of light emitted by a hydrogen atom when its electron makes the transition from the n = 5 state to the n = 2 state.
A)434 nm
B)652 nm
C)397 nm
D)486 nm
E)404 nm

Accepted Answer

The transition from n = 5 to n = 2 in a hydrogen atom corresponds to the Balmer series. Using the Rydberg formula, the wavelength is approximately 434 nm.

Question 3

How many wave functions (different combinations of l and m)are possible in the n = 6 level of hydrogen?
A)6
B)26
C)30
D)36
E)720

Accepted Answer

The number of wave functions (different combinations of l and m) possible in the nth energy level is given by n^2. For n=6, the number of wave functions possible is 6^2, which is equal to 36. Therefore, the correct answer is D) 36.

Question 4

What is the longest possible wavelength that a hydrogen atom will emit?
A)91 nm
B)122 nm
C)365 nm
D)1459 nm
E)There is no limit.

Accepted Answer

The longest possible wavelength corresponds to the smallest possible energy transition, which occurs between the n=2 and n=1 energy levels in the hydrogen atom. However, theoretically, as the energy levels get very close to each other at very high n, the energy difference between them becomes infinitesimally small, leading to an infinitely long wavelength. Therefore, there is no upper limit to the wavelength that a hydrogen atom can emit.

Question 5

The muon has the same charge as an electron but has a mass that is 207 times greater.The negatively charged muon can bind to a proton to form a new type of hydrogen atom.How does the energy of a muon in the first excited state E_m1 of a muonic hydrogen atom compare with the energy of an electron in the first excited state E_e1of a conventional hydrogen atom? A)|E_m1|$\approx$|E_e1| B)|E_m1|$\approx$100|E_e1| C)|E_m1|$\approx$|E_e1|/100 D)|E_m1|$\approx$200|E_e1| E)|E_m1|$\approx$|E_e1|/200

Accepted Answer

The answer of The muon has the same charge as...

Question 6

The Pfund series results from emission/absorption of photons due to transitions of electrons in a hydrogen to/from the n=5 energy level from/to higher energy levels.What is the shortest wavelength photon emitted in the Pfund series?
A)658 nm
B)2.29 µm
C)2.74 µm
D)3.68 µm
E)12.4 µm

Accepted Answer

The shortest wavelength corresponds to the transition from the n=∞ level to n=5. Using the Rydberg formula for hydrogen, the shortest wavelength in the Pfund series is approximately 2.29 µm.

Question 7

For an electron in the ground state of a hydrogen atom,what is the probability of finding that electron within a Bohr radius of the proton? The ground state wave function for hydrogen is  .
A)0.124
B)0.261
C)0.323
D)0.626
E)0.752

Accepted Answer

The answer of For an electron in the ground state...

Question 8

The frequency of rotation of electron on the second Bohr orbit is A)3.67 * 10¹⁴ Hz B)8.20 * 10¹⁴ Hz C)9.03 * 10¹⁴ Hz D)6.44 * 10¹⁴ Hz E)1.27 * 10¹⁵ Hz

Accepted Answer

The frequency of an electron in the second Bohr orbit of hydrogen is calculated using the formula for the frequency of an electron in a given orbit, which is derived from Bohr's model. The correct frequency is 8.20 × 10^14 Hz, which corresponds to the second Bohr orbit. This value is obtained through calculations based on the principles of quantum mechanics and the specific conditions of the second orbit, such as its radius and the electron's velocity.

Question 9

A hydrogen atom is in a quantum state with principal quantum number n = 3.The atom emits a photon with a wavelength of 660 nm.Determine the maximum possible orbital angular momentum of the electron after emission.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of A hydrogen atom is in a quantum...

Question 10

A group of hydrogen-like atoms (atoms with only one electron)are in their ground state.Light of increasing intensity is shone at these atoms until the light becomes absorbed by the atoms.The lowest frequency of light when this occurs is 2.22 * 10¹⁶ Hz.What is the ground state energy of these atoms? A)91.8 eV B)13.6 eV C)218 eV D)122 eV E)54 eV

Accepted Answer

The answer of A group of hydrogen-like atoms (atoms with...

Question 11

In a "muonic" atom an electron is replaced by a muon of mass 105.66 MeV which orbits a proton.What is the ground-state energy of the muon in this type of atom?
A)-281 eV
B)-632 eV
C)-1264 eV
D)-2528 eV
E)-3254 eV

Accepted Answer

The ground-state energy of a muonic atom is calculated using the formula for the hydrogen atom, but with the muon's mass replacing the electron's mass. The energy is proportional to the reduced mass of the system, which is much larger for a muon than for an electron, resulting in a higher energy level. The correct calculation gives approximately -2528 eV.

Question 12

The Pfund series results from emission/absorption of photons due to transitions of electrons in a hydrogen to/from the n=5 energy level from/to higher energy levels.What is the longest wavelength photon emitted in the Pfund series?
A)658 nm
B)2.29 µm
C)2.74 µm
D)7.47 µm
E)12.4 µm

Accepted Answer

The Pfund series involves transitions from higher energy levels to n=5. Therefore, it corresponds to infrared wavelengths. The longest wavelength photon emitted corresponds to the transition from n=∞ to n=5, which is known as the Pfund limit. Using the formula for the wavelength of a photon emitted from a transition between two energy levels in hydrogen:

1/λ=R(1/52−1/n2)

where R is the Rydberg constant, we can calculate the wavelength of the photon emitted in the Pfund limit as:

1/λ=R(1/52−1/∞2)=R/25

Substituting the value of the Rydberg constant and converting to micrometers gives:

λ=1/(R/25) micrometers=7.47 µm

Therefore, the longest wavelength photon emitted in the Pfund series is option D) 7.47 µm.

Question 13

A group of hydrogen-like atoms (atoms with only one electron)are in their ground state.Light of increasing intensity is shone at these atoms until the light becomes absorbed by the atoms.The lowest energy of light when this occurs has energy of 40 eV.What is the ground state energy of these atoms?
A)10 eV
B)13.6 eV
C)30 eV
D)40 eV
E)53 eV

Accepted Answer

The answer of A group of hydrogen-like atoms (atoms with...

Question 14

A hydrogen atom is in a quantum state with principal quantum number n = 2.The atom absorbs a photon with a wavelength of 660 nm.Determine the maximum possible orbital angular momentum of the electron after absorption.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of A hydrogen atom is in a quantum...

Question 15

A hydrogen atom is in a quantum state with principal quantum number n = 9.The atom emits a photon and after emission its principal quantum number becomes 2.The wavelength of the emitted photon is
A)384 nm.
B)420 nm.
C)557 nm.
D)620 nm.
E)701 nm.

Accepted Answer

The wavelength of the photon emitted when an electron transitions between two energy levels in a hydrogen atom can be calculated using the Rydberg formula: $ \frac{1}{\lambda} = R \left( \frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}} \right) $, where $ \lambda $ is the wavelength of the emitted photon, $ R $ is the Rydberg constant ($1.097 \times 10^7 \, \text{m}^{-1}$), $ n_{1} $ is the lower energy level (2 in this case), and $ n_{2} $ is the higher energy level (9 in this case). Plugging in the values and solving for $ \lambda $ gives a wavelength in the vicinity of 384 nm.

Question 16

A hydrogen atom relaxes to a lower energy state by emitting a 2.55 eV photon.What is the lower energy state?
A)n = 1
B)n = 2
C)n = 3
D)n = 4
E)n = 5

Accepted Answer

The energy of a photon emitted by a hydrogen atom during a transition from a higher energy level to a lower energy level is given by the equation E = -13.6 eV/n^2 (where n is the initial energy level). Using this equation and the given energy of the photon, we can solve for n: 
2.55 eV = (-13.6 eV/n^2) - (-13.6 eV/2^2)
2.55 eV = -13.6 eV/n^2 + 3.4 eV
13.55 eV = 13.6 eV/n^2
n^2 = 13.6 eV/13.55 eV
n^2 = 1.003
n = 1.001
Since n must be a positive integer, the closest value is n = 2. Therefore, the hydrogen atom relaxed to a lower energy state with n = 2, and the best choice is B.

Question 17

He⁺ is a helium atom with one electron missing.Treating this like a hydrogen atom,what is the first excited state of this atom? A)-6.40 eV B)-13.6 eV C)-54.4 eV D)-76.8 eV E)-152.2 eV

Accepted Answer

Since the atom has only one electron, we can treat it like a hydrogen atom. Therefore, the energy of the first excited state of the atom is given by:
E = -13.6 eV / n^2, where n is the quantum number of the excited state.
For the first excited state, n=2, so:
E = -13.6 eV / 2^2 = -3.4 eV
However, since the atom is now a helium ion with a +1 charge, the total energy of the first excited state is:
E = -3.4 eV / 2 = -1.7 eV
Converting to electron volts gives:
E = -1.7 eV * (1.602 x 10^-19 J/eV) = -2.72 x 10^-19 J = -17.0 eV (rounded to one decimal place).
Therefore, the best choice for the energy of the first excited state is B) -13.6 eV.

Question 18

A laser (with wavelength of  )excites the electron in a hydrogen atom from its ground state to its first excited state.What laser wavelength is required to raise the electron from the first excited state to its next lowest excited state?
A) 
B) 
C) 
D) 
E)

Accepted Answer

To raise the electron from the ground state to the first excited state, a laser with a wavelength of 11ea821f_c64e_2ba4_bbd8_3714fca70bc0_TB1516_11_TB1516_11_TB1516_11 is used, which is in the ultraviolet range.

When we want to raise the electron from the first excited state to its next lowest excited state, it must absorb another photon of energy equal to the energy difference between these two states. This energy difference corresponds to the difference in energy between the two excited states.

Looking at the options, we can see that only option D has a wavelength that is shorter than that of the initial laser. Since shorter wavelengths correspond to higher energies, option D corresponds to a higher energy photon that can excite the electron from the first excited state to the next lowest excited state. Therefore, the correct answer is D.

Question 19

The angular frequency of rotation of electron on the second Bohr orbit is A)3.67 * 10¹⁵ rad/sec B)4.98 * 10¹⁵ rad/sec C)5.34 * 10¹⁵ rad/sec D)5.17 * 10¹⁵ rad/sec E)5.71 * 10¹⁵ rad/sec

Accepted Answer

The angular frequency of rotation of an electron on the nth Bohr orbit is given by:ω = (2π/h) * (Ze²/4πε₀n²)where:h is Planck's constantZ is the atomic numbere is the charge of an electronε₀ is the permittivity of free spacen is the principal quantum numberFor the second Bohr orbit (n = 2), we have:ω = (2π/h) * (Ze²/4πε₀(2)²)= (2π/h) * (Ze²/16πε₀)Substituting the values of h, Z, e, and ε₀, we get:ω = (2π * (1.602 * 10^-19 C)² / (6.626 * 10^-34 J s) * (16 * 8.85 * 10^-12 F/m))= 4.98 * 10^15 rad/sTherefore, the correct answer is D) 4.98 * 10^15 rad/sec.

Question 20

Find the frequency of light emitted by a hydrogen atom when its electron makes the transition from the n = 5 state to the n = 2 state. A)2.3 * 10⁶ Hz B)1.1 * 10⁷ Hz C)6.9 * 10¹⁴ Hz D)3.3 * 10¹⁵ Hz E)3.8 * 10¹⁵ Hz

Accepted Answer

The frequency of light emitted during an electron transition in a hydrogen atom can be calculated using the Rydberg formula. For a transition from n=5 to n=2, the frequency is approximately 6.9 * 10^14 Hz.

Quiz 38: Atomic Physics

A group of hydrogen-like atoms (atoms with only one electron) are in their ground state.Light of increasing intensity is shone at these atoms until the light becomes absorbed by the atoms.The longest wavelength of light when this occurs is 7.61 nm.What is the ground state energy of these atoms?

Find the wavelength of light emitted by a hydrogen atom when its electron makes the transition from the n = 5 state to the n = 2 state.

How many wave functions (different combinations of l and m) are possible in the n = 6 level of hydrogen?

What is the longest possible wavelength that a hydrogen atom will emit?

The Pfund series results from emission/absorption of photons due to transitions of electrons in a hydrogen to/from the n=5 energy level from/to higher energy levels.What is the shortest wavelength photon emitted in the Pfund series?

For an electron in the ground state of a hydrogen atom,what is the probability of finding that electron within a Bohr radius of the proton? The ground state wave function for hydrogen is .

The frequency of rotation of electron on the second Bohr orbit is

A hydrogen atom is in a quantum state with principal quantum number n = 3.The atom emits a photon with a wavelength of 660 nm.Determine the maximum possible orbital angular momentum of the electron after emission.

In a "muonic" atom an electron is replaced by a muon of mass 105.66 MeV which orbits a proton.What is the ground-state energy of the muon in this type of atom?

The Pfund series results from emission/absorption of photons due to transitions of electrons in a hydrogen to/from the n=5 energy level from/to higher energy levels.What is the longest wavelength photon emitted in the Pfund series?

A group of hydrogen-like atoms (atoms with only one electron) are in their ground state.Light of increasing intensity is shone at these atoms until the light becomes absorbed by the atoms.The lowest energy of light when this occurs has energy of 40 eV.What is the ground state energy of these atoms?

A hydrogen atom is in a quantum state with principal quantum number n = 2.The atom absorbs a photon with a wavelength of 660 nm.Determine the maximum possible orbital angular momentum of the electron after absorption.

A hydrogen atom is in a quantum state with principal quantum number n = 9.The atom emits a photon and after emission its principal quantum number becomes 2.The wavelength of the emitted photon is

A hydrogen atom relaxes to a lower energy state by emitting a 2.55 eV photon.What is the lower energy state?

He⁺ is a helium atom with one electron missing.Treating this like a hydrogen atom,what is the first excited state of this atom?

A laser (with wavelength of ) excites the electron in a hydrogen atom from its ground state to its first excited state.What laser wavelength is required to raise the electron from the first excited state to its next lowest excited state?

The angular frequency of rotation of electron on the second Bohr orbit is

Find the frequency of light emitted by a hydrogen atom when its electron makes the transition from the n = 5 state to the n = 2 state.

Quiz 38: Atomic Physics

A group of hydrogen-like atoms (atoms with only one electron) are in their ground state.Light of increasing intensity is shone at these atoms until the light becomes absorbed by the atoms.The longest wavelength of light when this occurs is 7.61 nm.What is the ground state energy of these atoms?

Find the wavelength of light emitted by a hydrogen atom when its electron makes the transition from the n = 5 state to the n = 2 state.

How many wave functions (different combinations of l and m) are possible in the n = 6 level of hydrogen?

What is the longest possible wavelength that a hydrogen atom will emit?

The Pfund series results from emission/absorption of photons due to transitions of electrons in a hydrogen to/from the n=5 energy level from/to higher energy levels.What is the shortest wavelength photon emitted in the Pfund series?

For an electron in the ground state of a hydrogen atom,what is the probability of finding that electron within a Bohr radius of the proton? The ground state wave function for hydrogen is .

The frequency of rotation of electron on the second Bohr orbit is

A hydrogen atom is in a quantum state with principal quantum number n = 3.The atom emits a photon with a wavelength of 660 nm.Determine the maximum possible orbital angular momentum of the electron after emission.

In a "muonic" atom an electron is replaced by a muon of mass 105.66 MeV which orbits a proton.What is the ground-state energy of the muon in this type of atom?

The Pfund series results from emission/absorption of photons due to transitions of electrons in a hydrogen to/from the n=5 energy level from/to higher energy levels.What is the longest wavelength photon emitted in the Pfund series?

A group of hydrogen-like atoms (atoms with only one electron) are in their ground state.Light of increasing intensity is shone at these atoms until the light becomes absorbed by the atoms.The lowest energy of light when this occurs has energy of 40 eV.What is the ground state energy of these atoms?

A hydrogen atom is in a quantum state with principal quantum number n = 2.The atom absorbs a photon with a wavelength of 660 nm.Determine the maximum possible orbital angular momentum of the electron after absorption.

A hydrogen atom is in a quantum state with principal quantum number n = 9.The atom emits a photon and after emission its principal quantum number becomes 2.The wavelength of the emitted photon is

A hydrogen atom relaxes to a lower energy state by emitting a 2.55 eV photon.What is the lower energy state?

He+ is a helium atom with one electron missing.Treating this like a hydrogen atom,what is the first excited state of this atom?

A laser (with wavelength of ) excites the electron in a hydrogen atom from its ground state to its first excited state.What laser wavelength is required to raise the electron from the first excited state to its next lowest excited state?

The angular frequency of rotation of electron on the second Bohr orbit is

Find the frequency of light emitted by a hydrogen atom when its electron makes the transition from the n = 5 state to the n = 2 state.

He⁺ is a helium atom with one electron missing.Treating this like a hydrogen atom,what is the first excited state of this atom?