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Solved problems for the chapter:

Energy and Momentum of a Photon

View the theory »

Atomic Interaction with Photons

1. Spectrometer

2. Emission spectrum

2.1. Continuous emission spectrum

2.2. Line emission spectrum

3. Absorption spectrum

4. X-rays

5. Forum

View the theory »

Energy Levels of Atoms

1. Electron shells

2. Transitions between electron shells

3. Forum

↓ Show theory [2] ↓

Detailed solution steps are available at:

https://en.openprof.com/wb/chapter:energy_and_momentum_of_a_photon/4534/

Example 1.

Calculate the minimum wavelength of radiation emanating from an X-ray tube operating at 9000 V.

Note that:

Example 2.

Calculate the voltage at which an X-ray tube operates if it emits radiation with a minimum wavelength of 100 pm.

Note that:

An X-ray tube operates at a voltage of 10 kV. What is the energy of the photons emanating from this tube? Which part of the spectrum do they belong to?

Calculate the maximum frequency of radiation emanating from an X-ray tube operating at a voltage of 13500 V.

Note that:

The work function for electrons in a metal is equal to 26 eV. The surface of this metal is irradiated with X-rays. In doing so, electrons are emitted from the metal, the kinetic energy of which is measured. What is the maximum kinetic energy that the emitted electrons can have if the X-ray tube is operated at 1.2 kV?

A metal is irradiated with X-rays. The work function for the electrons of this metal is 9 eV. We measure that the ejected electrons have a speed of 50,000 km/s. What energy do X-rays have? What is the voltage in the X-ray tube to get these rays?

Note that:

If we reduce the voltage of an X-ray tube by 15 kV, the minimum wavelength of the emitted radiation increases becomes doubled. What is the initial and final minimum wavelength of radiation from this X-ray tube?

Note that:

The distance between adjacent atoms in the crystal lattice of a substance is 200 pm. What must be the voltage of the X-ray tube in order to feel the structure of the crystal with X-rays?

Note that:

In an X-ray tube, an electron emitted by the cathode is accelerated with a voltage of 19 kV. The electron collides with the anode and excites one of its atoms. Assume that the electron gives all its energy to the atom. This atom then returns to its ground state by emitting one photon.

How many joules is the energy of the photon emitted by the atom on its return to the ground state?
What energy does the atom in the anode receive from the electron?
What is the velocity of the emitted photon?
Which part of the electromagnetic wave spectrum does this photon belong to?

Take:

10.

An unexcited hydrogen atom with a kinetic energy of 15 eV collides with a stationary hydrogen atom in the ground state. The collision of the atoms is inelastic and after the collision, the stationary hydrogen atom jumps into the first excited state and is still stationary. Calculate the kinetic energy of the first atom after the collision.

The ground state energy of a hydrogen atom is .

11.

An electron with a kinetic energy of 17.5 eV collides with a stationary hydrogen atom. The ground state energy of an electron of a hydrogen atom is . After the collision, the atom is still stationary, and the electron still has 4.75 eV of kinetic energy. In what excited state is the hydrogen atom after the collision?

12.

An electron in an atom has passed into a state with an energy of 0 eV. Find out which of the following statements is correct and explain why.

The electron hit the atomic nucleus.
The electron went into a lower energy state by emitting a photon.
Photon collided with the electron and handed over its energy to it.
This electron collided with another electron and died.

13.

The energy of the ground electronic state in a hydrogen atom is . What is the wavelength of the wave that is required to ionize the hydrogen atom?

14.

An electron in a hydrogen atom is in the first excited state with the energy of . What can be the wavelength of the emitted photon when the electron enters another energy state?

15.

A hydrogen atom and a once ionized helium atom have one outer electron. We knock out this one outer electron in each of them using some energy.

Choose the correct statement about the energy with the correct explanation from the list below:

The energy consumed is the same for hydrogen and helium since in both cases, we emit one electron.
The energy consumed is higher with helium, as it has two more neutrons in the nucleus as opposed to hydrogen, which has none.
The energy consumed is higher with hydrogen as the electron orbits at a greater distance from the nucleus.
The energy consumed is higher in helium because it has more nucleons in the nucleus than hydrogen.
The energy consumed is higher in helium as it has more protons than hydrogen.
The energy consumed is higher with hydrogen as hydrogen is lighter and has higher kinetic energy.

16.

In the helium ion is an electron in the ground state with an energy of . The first three excited states have , and , respectively. Determine the state of the electron after it absorbs a photon with a wavelength of . Can this excited electron emit visible light?

17.

A gas atom has an energy spectrum with the following values , , , , and .

Between which energy states does it pass when it absorbs photons with an energy of ?
What frequency does the photon emit if it then transits from the excited state to the ground state?

(Note: )

18.

We have a hydrogen atom, with an electron in the ground state at an energy of . What does ionization energy mean and how much is it in this case? Choose the correct explanation and the correct value from the list below:

Ionization energy is the electron energy of .
Ionization energy is the energy of the first excited state and is .
Ionization energy means the energy lost by the atom in a collision with another atom and amounts to .
Ionization energy is the energy required to convert the atom into an ion and is .
Ionization energy is the energy of an ion and is .
Ionization energy is the energy of an ion and is .
Ionization energy is the energy required to convert the atom to an isotope and is .

19.

The sodium atom has an ionization energy of . This is the energy needed to knock an outer electron in the ground state out of the sodium atom. Sodium ion is obtained in the transition of an outer electron from the first excited state to the ground state alongside light with a wavelength of . What kind of light do we need to ionize a sodium atom that has an outer electron in the first excited state?

20.

An electron is in the second excited state in one atom.

What are the wavelengths of the photons it can emit?
What are the wavelengths of the photons it can absorb?

Consider electron transitions within the following energy states:

, , , and

21.

In a hydrogen atom, an electron in the ground state has an energy of . In a once ionized helium atom , however, the remaining electron has an energy of in the ground state. Calculate by what factor the energies of the ground states of the two atoms differ.

()

22.

What is the wavelength of the photon obtained by the transition of an electron in a hydrogen atom from the state with the principal quantum number to the first excited state?

In which part of the spectrum does the resulting photon wavelength fall if the energy of the electron in the ground state of hydrogen is .

23.

What is the frequency of the photon needed to ionize a hydrogen atom with an electron in the second excited state? In the ground state, the electron of a hydrogen atom has an energy of . The speed of light is , the Planck constant .

24.

Electronic states in a hydrogen atom have the following energies , , , ... An electron is in the third excited state, what are the possible wavelengths of the emitted photon when the electron transitions to a lower state?