12.1 The Interaction of Matter with Radiation

A vacuum photocell is connected in series with a power supply, a variable resistor, and a sensitive ammeter. A voltmeter is connected in parallel across the photocell.

Monochromatic light of frequency f illuminates the cathode, which has a threshold frequency f₀. Photoelectrons are emitted and collected by the anode. A photocurrent is measured by the ammeter.

The potential difference across the photocell, V, is increased until the ammeter reads zero. 

Which of the equations below does not correctly relate the potential V at which the current decreases to zero to the threshold frequency f₀ and frequency f?

The first three wavefunctions are shown for a particle confined in a box of length L.

For which wave function is the probability of finding the particle near the smallest?

A beam of electrons of wavelength λ is incident on an aperture of width d. The beam is travelling along the z direction. The width d is of a size comparable to λ. 

After passing through the aperture, the component of momentum in the x direction is p_x, the component in the y direction is p_y and the component in the z direction is p_z.

Which of the following shows the uncertainty in p_x, p_y and p_z? 

	Δpx	Δpy	Δpz
A.
B.			0
C.	0	0
D.	0		0

In 1890 Johannes Rydberg discovered an empirical formula that enabled the wavelengths of the light in the atomic line spectrum of hydrogen to be calculated. The formula is:

Where λ is the wavelength, n and m are integers and R_H is the Rydberg constant.

In 1913 Niels Bohr published his theory of the hydrogen atom. This theory enabled the Rydberg formula to be derived. His theory also showed that the energy levels E_n of the hydrogen atom are given by the formula: 

Where E_n is measured in joules. 

Which of the following is a valid expression for the Rydberg constant?

An electron is confined to a box. The energy difference between the first and the fourth states is 15.0 eV.

Which would be the best order of magnitude estimate for the length of the box?

A square plate made of zinc with side length d is given a charge of Q and then illuminated with an ultraviolet lamp of wavelength λ. The lamp has an output power of 100 W.

The lamp is placed a distance r above the surface and positioned such that the UV light is incident normally on the zinc surface.

Which of the following is the correct expression for the time taken for the zinc plate to become electrically neutral?

An alpha particle with energy E is incident upon a potential barrier and has a certain probability of quantum tunnelling through the barrier.

Consider the following statements:

I. The energy of the alpha particle is increased

II. The width of the potential barrier is increased

III. The alpha particle is replaced by an electron with energy E

Which statements would lead to an increase in the probability of finding a particle that has escaped a potential barrier?

Consider the following statements regarding the Bohr model of the hydrogen atom:

Which statements originate from the idea that the circumference of the orbit must be an integer number of the de Broglie wavelength?

An atom in an excited state has an orbital radius of 10⁻¹² m.

Which would be the best order of magnitude estimate for the energy of this state according to the uncertainty principle?

Violet light is incident on a metal surface, producing photoelectrons. 

The variation of photocurrent I with potential difference V is shown. 

The light source is changed to red light of the same intensity as the violet light. Which graph shows the variation of photocurrent I with potential difference V for the red light? The results for the violet light are shown as a dashed line. 

Which expression is proportional to the probability of finding an electron in a particular region of space? 

The graphs show the variation with distance  of the square of the magnitude of the wave function, , of a particle. Which graph corresponds to a particle with the largest uncertainty in momentum? 

The graph shows how the wave function Ψ of an electron varies with distance x. 

Which of the following graphs shows the probability  of finding the electron at each position along the distance x?

According to Heisenberg's uncertainty principle, conjugate quantities are pairs of quantities that cannot be known simultaneously with unlimited precision. What unit represents the product of two conjugate quantities?  

Alpha particles of mass m are accelerated from rest through a potential difference ΔV. Which of the following gives the de Broglie wavelength of the alpha particles as a result of the acceleration? 

Use the following data: 

• Planck's constant is h
• The magnitude of charge on an electron is e

Which expression evaluates the de Broglie wavelength of an electron of mass m and charge e in the n = 2 state of hydrogen? 

The electron wave function Ψ is a function of position and time. Which expression evaluates the probability of discovering the electron in some volume ΔV?  

According to the Bohr model for hydrogen, visible light is emitted when electrons make transitions from excited states down to the state with n = 2. 

The dotted line in the diagram represents such a transition, from n = 3 to n = 2, in the spectrum of hydrogen. 

Which of the following diagrams could represent the visible light emission spectrum of hydrogen?