Quantum Physics

State what is meant by a photon.

Calculate the wavelength of the light.

wavelength = ______ $\text{m}$

The power of the beam emitted by the laser is $1.0 \times 10^{-2}\ \text{W}$.

Calculate the number of photons emitted per unit time by the laser.

number per unit time = ______ $\text{s}^{-1}$

The photons are incident normally on a surface. Half of the number of photons are absorbed by the surface, and half are reflected.

Determine the average force exerted by the beam of photons on the surface.

average force = ______ $\text{N}$

State what is meant by the photoelectric effect.

Explain, with reference to photons, why $V_S$ depends on the frequency of the incident electromagnetic radiation.

State three quantitative conclusions that can be drawn from the results in Fig. 9.2 and Fig. 9.3. Use the space for any working.

Describe what is meant by wave–particle duality.

State the relationship between the de Broglie wavelength $\lambda$ of a particle and its momentum $p$. State the meaning of any other symbols that you use.

Explain why the pattern in Fig. 9.2 provides experimental evidence to indicate a wave nature for the electrons.

The speed of the electrons is increased.

Suggest, with a reason, how this change affects the pattern observed on the screen.

Use the photon model of electromagnetic radiation to explain how the existence of spectral lines in the emission spectrum provides evidence for discrete electron energy levels in the hydrogen atom.

Calculate the energy, in $\text{J}$, of the ground state.

$\text{energy}$ = ______ $\text{J}$

Show that the energy difference between levels $n = 1$ and $n = 2$ is $10.2\text{ eV}$.

Complete Table 8.1 to show the energy differences from the ground state, and the energies of the levels up to $n = 4$, in the hydrogen atom. Use the space for any working.

Table 8.1

State what is meant by the photoelectric effect.

the threshold frequency of metal Y

threshold frequency = ______

the Planck constant.

Planck constant = ______

The maximum kinetic energy $E_K$ of photoelectrons is determined for each of the plates in (b) for different frequencies $f$ of incident radiation.

On Fig. 9.1, sketch the variation of $E_K$ with $f$ for each plate. Label your lines X and Y to identify which line relates to which plate.

A photon has an energy of $3.11 \times 10^{-19} \text{ J}$.

Calculate the momentum of the photon.

momentum = ______ $\text{Ns}$

Determine the number of photons emitted by the laser in a time of $1.0 \text{ s}$.

number = ______

The laser beam is incident normally on a surface that absorbs all of the photons.

Show that the force $F$ exerted on the surface by the laser beam is given by

where $P$ is the power of the laser beam and $c$ is the speed of light.

Explain the term threshold wavelength.

For the metals in Table 7.1, calculate the value of the largest threshold wavelength.

threshold wavelength = ______ $\text{m}$

State the name of this phenomenon.

Calculate the work function energy of magnesium.

work function energy = ______ $\text{J}$

For ultraviolet radiation with a frequency of $11 \times 10^{14}\ \text{Hz}$, calculate the maximum speed of the emitted electrons.

maximum speed = ______ $\text{m s}^{-1}$

The frequency $f$ of the ultraviolet radiation incident on the magnesium sheet is varied between $8.0 \times 10^{14}\ \text{Hz}$ and $11 \times 10^{14}\ \text{Hz}$.

On Fig. 8.1, sketch the variation with $f$ of the maximum kinetic energy $E_{MAX}$ of the emitted electrons. Use the space below for any working that you need.

State the name of this phenomenon.

Calculate the work function energy of magnesium.

work function energy = ______ $\text{J}$

For ultraviolet radiation with a frequency of $11 \times 10^{14}\ \text{Hz}$, calculate the maximum speed of the emitted electrons.

maximum speed = ______ $\text{m s}^{-1}$

The frequency $f$ of the ultraviolet radiation incident on the magnesium sheet is varied between $8.0 \times 10^{14}\ \text{Hz}$ and $11 \times 10^{14}\ \text{Hz}$.

On Fig. 8.1, sketch the variation with $f$ of the maximum kinetic energy $E_{MAX}$ of the emitted electrons. Use the space below for any working that you need.

A beam of white light passes through a cloud of cool gas. The spectrum of the transmitted light is viewed and contains a number of dark lines.

Explain why these dark lines occur.

Some energy levels for the electron in an isolated hydrogen atom are illustrated in Fig. 7.1.

Table 7.1 shows the wavelengths of photons that are emitted in the transitions to $n = 2$ from the other energy levels shown in Fig. 7.1.

Table 7.1

The energy associated with the energy level $n = 2$ is $-3.40\ \text{eV}$.

Calculate the energy, in J, of energy level $n = 3$.

energy = ______ $\text{J}$

State what is meant by the de Broglie wavelength.

State the name of the phenomenon demonstrated by the pattern shown in Fig. 7.2.

Explain what can be concluded from the pattern in Fig. 7.2 about the nature of electrons.

On Fig. 7.3, sketch the pattern that is now seen on the fluorescent screen in Fig. 7.1.

Explain, with reference to de Broglie wavelength, the change in the pattern on the fluorescent screen.