12.1 The Interaction of Matter with Radiation

Question 1

Marks: 1

An electron in a one-dimensional box, known as the “electron in a box” model, is a fundamental quantum mechanical approximation describing the translational motion of a single electron confined inside an infinitely deep well from which it cannot escape.

According to the “electron in a box” model, which of the following expressions is not a permitted value for the momentum of an electron moving in a box of length L?

$\frac{h}{4 L}$
$\frac{3 h}{2 L}$
$\frac{3 h}{L}$
$\frac{4 h}{L}$

Key Concepts

The Wave Function
Quantization of Angular Momentum

Question 2

Marks: 1

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.

q28_the-photoelectric-effect_aqa-as-physics-mcq

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?

$V = \frac{h}{e} (f - f_{0})$
$f_{0} = \frac{h f - e V}{h}$
$h = \frac{e V}{(f - f_{0})}$
$V = \frac{e}{h f_{0} - h f}$

Key Concepts

Solving Photoelectric Problems

Question 3

Marks: 1

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

ubBA9nmv_wavefunction-probability

For which wave function is the probability of finding the particle near $x = \frac{L}{2}$ the smallest?

n = 1
n = 2
n = 3
The probability is the same (and non-zero) for each wavefunction

Key Concepts

The Wave Function

Question 4

Marks: 1

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.

E87kCd~j_single-slit-uncertainty-mcq

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?

	Δp_x	Δp_y	Δp_z
A.	$\frac{h}{4 π d}$	$\frac{h}{4 π d}$	$\frac{h}{4 π d}$
B.	$\frac{h}{4 π d}$	$\frac{h}{4 π d}$	0
C.	0	0	$\frac{h}{4 π d}$
D.	0	$\frac{h}{4 π d}$	0

Key Concepts

The Uncertainty Principle

Question 5

Marks: 1

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:

$\frac{1}{λ} = R_{H} (\frac{1}{n^{2}} - \frac{1}{m^{2}})$

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:

$E_{n} = \frac{2.2 \times 10^{- 18}}{n^{2}}$

Where E_n is measured in joules.

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

$R_{H} = 2.2 \times 10^{- 18}$
$R_{H} = \frac{2.2 \times 10^{- 18}}{h c (1 - \frac{n^{2}}{m^{2}})}$
$R_{H} = \frac{2.2 \times 10^{- 18}}{h c}$
$R_{H} = 2.2 \times 10^{- 18} (\frac{n^{2} - m^{2}}{m^{2} - n^{2}})$

Key Concepts

Quantization of Angular Momentum

Question 6

Marks: 1

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?

10⁻⁹ m
10⁻¹⁰ m
10⁻¹¹ m
10⁻¹² m

Key Concepts

The Wave Function
Quantization of Angular Momentum

Question 7

Marks: 1

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?

$\frac{h c}{100 e} (\frac{Q}{λ d^{2}})$
$\frac{h c}{100 e} (\frac{Q}{λ r^{2}})$
$\frac{h c}{25 π e} (\frac{Q d^{2}}{λ r^{2}})$
$\frac{π h c}{25 e} (\frac{Q r^{2}}{λ d^{2}})$

Key Concepts

Solving Photoelectric Problems

Question 8

Marks: 1

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?

I and II only
I and III only
II and III only
I, II and III

Key Concepts

Tunnelling

Question 9

Marks: 1

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

The momentum of an electron is equal to the Planck constant divided by its de Broglie wavelength

II.

The angular momentum of the atom is quantised

III.

The energy levels are quantised

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

I and II only
I and III only
II and III only
I, II and III

Key Concepts

Quantization of Angular Momentum

Question 10

Marks: 1

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?

10¹ eV
10³ eV
10⁶ eV
10¹⁰ eV

Key Concepts

The Uncertainty Principle

DP IB Physics: HL

Topic Questions

12.1 The Interaction of Matter with Radiation

Question 1

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Question 2

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Question 3

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Question 4

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Question 5

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Question 6

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Question 7

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Question 8

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Question 9

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Question 10

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