7.1 Discrete Energy & Radioactivity

1a 1b 1c 1d 2a 2b 2c 2d 3a 3b 4a 4b 4c 4d

Question 1a

Marks: 3

Transitions between three energy levels in a particular atom give rise to three spectral lines. In decreasing magnitudes, these are $f_{1}$ , $f_{2}$ and $f_{3}$ .

The equation which relates $f_{1}$ , $f_{2}$ and $f_{3}$ is:

$f_{1} = f_{2} + f_{3}$

(a)

Explain, including through the use of a sketch, how this equation relates

f_{1}

f_{2}

and

f_{3}

[3]

Key Concepts

Discrete Energy Levels
Transitions Between Energy Levels

Question 1b

Marks: 5

A different atom has a complete line emission spectra with a ground state energy of –10.0 eV. is:

7-1-ib-sl-hard-sqs-q1b-question

(b)

Sketch and label a diagram of the possible energy levels for the atomic line spectra shown.

[5 marks]

Key Concepts

Transitions Between Energy Levels
Discrete Energy Levels

Question 1c

Marks: 3

(c)

Explain the significance of an electron at an energy level of 0 eV.

[3]

Key Concepts

Discrete Energy Levels

Question 1d

Marks: 3

(d)

(i)

Explain the statement 'the first excitation energy of the hydrogen atom is 10.2 eV'

[1]

(ii)

The ground state of hydrogen is –13.6 eV. Calculate the speed of the slowest electron that could cause this excitation of a hydrogen atom.

[2]

Key Concepts

Discrete Energy Levels
Transitions Between Energy Levels

Question 2a

Marks: 2

A radioactive nucleus ${}_{85}^{229}X$ undergoes a beta−minus decay followed by an alpha decay to form a daughter nucleus ${}_{Z}^{A}Y$ .

(a)

Write a decay equation for this interaction and hence determine the values of A and Z.

[2]

Key Concepts

Radioactive Decay
Decay Equations

Question 2b

Marks: 3

Thorium, ${}_{232}^{90}{Th}$ decays to an isotope of Radium (Ra) through a series of transformations. The particles emitted in successive transformations are:

$α β β γ α$

(b)

Determine the resulting nuclide after these successive transformations.

[3]

Key Concepts

Isotopes
Decay Equations

Question 2c

Marks: 3

Through a combination of successive alpha and beta decays, the isotope of any original nucleus can be formed.

(c)

Explain the simplest sequence of alpha and beta decays required to do this

[3]

Key Concepts

Decay Equations

Question 2d

Marks: 2

A nucleus of Bohrium ${}_{Y}^{X}{Bh}$ decays to Mendelevium ${}_{101}^{255}{Md}$ by a sequence of three alpha particle emissions.

(d)

Determine the number of neutrons in a nucleus of

{}_{Y}^{X}{Bh}

[2]

Key Concepts

Decay Equations

Question 3a

Marks: 3

The table shows some of the isotopes of phosphorus and, where they are unstable, the type of decay.

Isotope	${}_{15}^{29}P$	${}_{15}^{30}P$	${}_{15}^{31}P$	${}_{15}^{32}P$	${}_{15}^{33}P$
Type of decay	$β^{+}$	$β^{+}$	stable		$β^{-}$

(a)

State whether the isotope ${}_{15}^{32}P$ is stable or not. If not, determine, with a reason, the type of decay it experiences.

[3]

Key Concepts

Alpha, Beta & Gamma Particles

Question 3b

Marks: 3

The isotope of phosphorus ${}_{15}^{30}P$ decays into an isotope of silicon, ${}_{Z}^{A}{Si}$ .

(b)

Write a decay equation for this decay, finding the values of A and Z, and explain why each emission product occurs.

[3]

Key Concepts

Decay Equations

Question 4a

Marks: 2

The radioactive isotope uranium−238 decays in a decay series to the stable lead−206.

The half−life of ${}_{92}^{238}U$ is 4.5 × 10⁹ years, which is much larger than all the other half−lives of the decays in the series.

A rock sample, when formed originally, contained 6.0 × 10²² atoms of ${}_{92}^{238}U$ and no ${}_{82}^{206}{Pb}$ atoms. At any given time, most of the atoms are either ${}_{92}^{238}U$ or ${}_{82}^{206}{Pb}$ with a negligible number of atoms in other forms in the decay series.

(a)

Sketch on the axes below the variation of number of

{}_{92}^{238}U

atoms and the number of

{}_{82}^{206}{Pb}

atoms in the rock sample as they vary over a period of 1.0 × 10¹⁰ years from its formation. Label your graphs U and Pb.

[2]

Key Concepts

Half-Life
Decay Curves

Question 4b

Marks: 2

A certain time, t, after its formation, the sample contained twice as many ${}_{92}^{238}U$ atoms as ${}_{82}^{206}{Pb}$ atoms.

(b) Show that the number of ${}_{92}^{238}U$ atoms in the rock sample at time t was 4.0 × 10²².

[2]

Key Concepts

Half-Life

Question 4c

Marks: 2

The ratio of the number of lead nuclei $N_{P b}$ to the number of uranium nuclei $N_{U}$ at some time t is given by:

$\frac{N_{P b}}{N_{U}} = e^{λ t} - 1$

λ is the decay constant and has a value of 1.54 × 10⁻¹⁰ years.

(c)

Calculate the time taken (in years) for there to be twice as many

{}_{92}^{238}U

atoms as

{}_{82}^{206}{Pb}

atoms.

[2]

Key Concepts

Decay Curves

Question 4d

Marks: 4

Lead−214 is an unstable isotope of lead−206. It decays by emitting a $β^{-}$ particle to form bismuth−214 (Bi)

Bismuth is also unstable and has two decay modes:

Emitting an α particle to form thallium−210 (Tl) + energy
Emitting a β particle to form polonium−214 (Po) + energy

(d)

Write decay equations for the decay chain of lead−214 to thallium−210 and to polonium−214. Comment on the nature of the energy released.

[4]

Key Concepts

Decay Equations

DP IB Physics: HL

Topic Questions

7.1 Discrete Energy & Radioactivity

Question 1a

Key Concepts

Question 1b

Key Concepts

Question 1c

Key Concepts

Question 1d

Key Concepts

Question 2a

Key Concepts

Question 2b

Key Concepts

Question 2c

Key Concepts

Question 2d

Key Concepts

Question 3a

Key Concepts

Question 3b

Key Concepts

Question 4a

Key Concepts

Question 4b

Key Concepts

Question 4c

Key Concepts

Question 4d

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