Worksheet: Atomic Spectra and Energy Levels

In this worksheet, we will practice comparing the Balmer, Lyman, and various X-ray series to the emission spectra of electron energy level transitions.

Q1:

Calculate the wavelength of the first line in the Lyman series. The Rydberg constant 𝑅 = 1 . 0 9 7 3 7 Γ— 1 0 H 7 βˆ’ 1 m . State you answer to four significant figures.

Q2:

In a hydrogen atom, an electron in its ground state has an energy 𝐸 = βˆ’ 1 3 . 6 0 e V . 0.850 eV was required to remove an electron from a hydrogen atom. What number state was the atom in before the ionization occurred?

Q3:

The energy of an electron in its ground state in a hydrogen atom is βˆ’ 1 3 . 6 eV. A photon of wavelength 700 nm is incident on a hydrogen atom. When this photon is absorbed, the atom becomes ionized. What is the lowest energy level that the electron could have occupied before being ionized?

Q4:

Find the shortest wavelength in the Balmer series, recalling that the Rydberg constant is 1 . 0 9 7 3 7 Γ— 1 0 βˆ’ 7 βˆ’ 1 m .

Q5:

In a hydrogen atom, an electron in its ground state has an energy 𝐸 = βˆ’ 1 3 . 6  e V . An emission line of atomic hydrogen with a wavelength of 4.653 ΞΌm corresponds to transition between the final state 𝑛 = 5  and initial state 𝑛  . Find 𝑛  .

Q6:

In a hydrogen atom, an electron in its ground state has an energy 𝐸 = βˆ’ 1 3 . 6 0 e V . What is the frequency of the photon absorbed when the hydrogen atom makes the transition from the ground state to the 𝑛 = 4 state?

Q7:

How many times smaller are the wavelengths of X-ray photons produced by gold than those produced by copper?

Q8:

The maximum characteristic X-ray photon energy comes from the capture of a free electron into a 𝐾 shell vacancy. What is this photon energy in keV for tungsten, assuming that the free electron has no initial kinetic energy?

Q9:

In a hydrogen atom, an electron in its ground state has an energy 𝐸 = βˆ’ 1 3 . 6 0 e V . A hydrogen atom is in its third excided state.

What is the shortest wavelength photon that the atom can emit?

What is the longest wavelength photon that the atom can emit?

Q10:

In a hydrogen atom, an electron in its ground state has an energy 𝐸 = βˆ’ 1 3 . 6 0 e V . An electron in a hydrogen atom is in the 𝑛 = 2 state.

Calculate the electron’s kinetic energy.

Calculate the electron’s potential energy.

Calculate the electron’s total energy.

Q11:

An electron in an atom is modeled as if it were confined to a box of width 2 . 0 Γ— 1 0 βˆ’ 1 0 m.

What is the ground state energy of the electron?

What percent of the ground state energy of the electron modeled using Bohr’s atomic model is the ground state energy of the electron modeled as being confined to a box?

Q12:

An atom can be formed when a negative muon is captured by a proton. The muon has the same charge as the electron and a mass 207 times that of the electron. Calculate the frequency of the photon emitted when this atom makes the transition from 𝑛 = 2 to the 𝑛 = 1 state. Assume that the muon is orbiting a stationary proton.

  • A 5 . 5 Γ— 1 0 1 7 Hz
  • B 4 . 5 Γ— 1 0 1 7 Hz
  • C 6 . 0 Γ— 1 0 1 7 Hz
  • D 5 . 1 Γ— 1 0 1 7 Hz
  • E 6 . 6 Γ— 1 0 1 7 Hz

Q13:

An electron in a ruby laser emits light that has a wavelength of 694.3 nm. What is the difference in energy of the electron’s state before and after emitting the light?

Q14:

In a hydrogen atom, an electron in its ground state has an energy 𝐸 = βˆ’ 1 3 . 6 0 e V .

Calculate the energy change corresponding to the transition of the hydrogen atom from the 𝑛 = 3 state to the 𝑛 = 4 state.

Calculate the energy change corresponding to the transition of the hydrogen atom from the 𝑛 = 2 state to the 𝑛 = 1 state.

Calculate the energy change corresponding to the transition of the hydrogen atom from the 𝑛 = 3 state to the 𝑛 = ∞ state.

Q15:

What is the ratio of the wavelengths of X-ray photons produced by silver and by copper?

Q16:

Determine the wavelength of the fifth Balmer line, the transition from 𝑛 = 7 to 𝑛 = 2 . Give your answer to three significant figures.

Q17:

A doubly ionized atom of lithium Li 2+ is a hydrogen-like ion. When Li 2+ is in one of its excited states, its radius in this 𝑛 th state is the same as the radius of the first Bohr’s orbit of hydrogen. The atomic number of Li is 3.

Find 𝑛 .

Find the ionization energy for this state of Li 2+. Give your answer to three significant figures.

Q18:

Find the ionization energy of a hydrogen atom in the third energy state. Give your answer to two significant figures.

Q19:

Find the radius of a hydrogen atom when the electron is in the second excited state. Give your answer to three significant figures.

  • A 5 . 0 2 Γ— 1 0 βˆ’ 1 0 m
  • B 3 . 1 7 Γ— 1 0 βˆ’ 1 0 m
  • C 1 . 5 0 Γ— 1 0 βˆ’ 1 0 m
  • D 4 . 7 6 Γ— 1 0 βˆ’ 1 0 m
  • E 4 . 6 7 Γ— 1 0 βˆ’ 1 0 m

Q20:

Calculate the wavelength of the fourth line in the Lyman series. Give your answer to three significant figures.

Q21:

A nitrogen atom can hybridize in the 𝑠 𝑝 2 configuration. What is the angle between the hybrid orbitals?

Q22:

The electron configuration of oxygen is 1s2 2s2 2p4. Given this electron configuration, which of the following elements can exhibit all of oxygen’s hybridization modes?

  • ACl
  • BNa
  • CNe
  • DN
  • ELi

Q23:

The ion B e 3 + makes an atomic transition from an β€œ 𝑛 = 4 ” state to an β€œ 𝑛 = 1 ” state and emits a photon.

What is the energy of the photon, to three significant figures?

What is the wavelength of the photon, to three significant figures?

Q24:

For 𝑛 = 1 , which of the following correctly shows the possible sets of quantum numbers ( 𝑛 , 𝑙 , π‘š , π‘š  )?

  • A ο€Ό 1 , βˆ’ 1 , 0 , 1 2  , ο€Ό 1 , βˆ’ 1 , 0 , βˆ’ 1 2 
  • B ο€Ό 1 , 1 , 0 , 1 2  , ο€Ό 1 , 1 , 0 , βˆ’ 1 2 
  • C ο€Ό 1 , 1 , 1 , 1 2  , ο€Ό 1 , 1 , 1 , βˆ’ 1 2 
  • D ο€Ό 1 , 0 , 0 , 1 2  , ο€Ό 1 , 0 , 0 , βˆ’ 1 2 
  • E ο€Ό 1 , 1 , βˆ’ 1 , 1 2  , ο€Ό 1 , 1 , βˆ’ 1 , βˆ’ 1 2 

Q25:

In an atom, a subshell of the 𝑛 = 4 shell contains 9 electrons.

What is the minimum value of the azimuthal quantum number 𝑙 for the subshell?

Which of the following is the spectroscopic notation for this atom?

  • A 4 𝑑 
  • B 3 𝑔 
  • C 4 β„Ž 
  • D 4 𝑔 
  • E 3 𝑑 

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