Nuclear Physicsname

Nuclear PhysicsName:

1.The following are statements concerning radioactive decay.

I.Alpha particles have discrete energies.

II.The beta-energy spectrum is a broad continuous distribution of energies.

III.Gamma rays are emitted with discrete energies.

Which statement(s) is(are) evidence for the existence of nuclear energy levels?

A.I only

B.II only

C.III only

D.I and III only

(1)

2.Some of the energy levels of the hydrogen atom are shown below.

–––––––––––––– – 0.54 eV
–––––––––––––– – 0.85 eV

–––––––––––––– – 1.51 eV

–––––––––––––– – 3.39 eV

–––––––––––––– – 13.6 eV

Electrons are excited to the 0.85 eV level. How many different photon frequencies will be observed in the emission spectrum of hydrogen?

A.3

B.4

C.5

D.6

(1)

3.In a mass spectrograph, ions of isotopes of the same element follow different semicircular paths in a uniform magnetic field as shown below.

The difference in path curvature is essentially due to the fact that the ions have different values of

A.charge only.

B.mass only.

C.mass and charge.

D.mass and speed.

(1)

4.The masses of nuclei in a sample of uranium are determined using a mass spectrometer. Measurements suggest that some nuclei in the sample have double the mass of others.

Which of the following is the most likely explanation for this observation?

A.Uranium nuclei are decaying radioactively.

B.Several uranium isotopes are present.

C.The uranium ions have different speeds.

D.The uranium ions have different charges.

(1)

5.The ratio of mass-to-charge was measured for a sample of a pure element in a mass spectrometer.
The values obtained were

17.518.535.037.0

where is the mass-to-charge ratio for a hydrogen () nucleus. The data suggest that two isotopes are present with masses

A.17.5u and 18.5u.

B.17.5u and 37.0u.

C.18.5u and 5.0u.

D.35.0u and 37.0u.

(1)

6.A free electron is confined within a one dimensional region of fixed length. Which of the diagrams below shows the four lowest energy levels of the electron?

(1)

7.This question is about the de Broglie hypothesis and the uncertainty principle.

According to the de Broglie hypothesis, all particles have an associated wavelength that is related to the momentum of the particle.

By considering a particle that has a precisely defined wavelength, describe how the de Broglie hypothesis relates to the Heisenberg uncertainty principle.

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(Total 3 marks)

8.This question is about a model of the atom.

The Schrödinger model of the atom pictures electrons as clouds of negative charge surrounding the nucleus. The distribution of charge and mass can be represented by a three-dimensional standing wave.

(a)Identify the feature of the standing wave that gives the probability of finding the electron at a particular position.

(2)

An electron of mass m in an atom has total energy E, potential energy EPand kinetic energy Ek

(b)Write down expressions for

(i)the relation between E, EP and EK.

(ii)the momentum p of the electron in terms of EK.

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(1)

(iii)the associated wavelength λ of the electron in terms of its total energy E.

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(2)

(Total 6 marks)

9.This question is about a mass spectrometer.

(a)State the purpose of a mass spectrometer.

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(1)

(b)In the space below, draw a schematic labelled diagram of a mass spectrometer.

(4)

(c)A pure sample of a gaseous element is examined using a mass spectrometer. Atomic masses of 35 u and 37 u are obtained. Chemical analysis of a similar sample of the gas suggests an atomic mass of 35.5 u. Determine the ratio, for this sample,

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(4)

(Total 9 marks)

10.This question is about the Bohr model of the hydrogen atom and the Heisenberg uncertainty principle.

(a)A postulate of the Bohr model of the hydrogen atom is that the electron revolves about the proton in stable, circular orbits. State two other postulates of the Bohr model.

In the nthenergy state, the hydrogen atom has energy Enand the electron orbits with speed vnin an orbit of radius rn. En, rnand vnare given by the following relationships.

En= –eV

rn= 0.0529n2 nm

vn= m s–1

(b)Apply the expressions above, to hydrogen in its ground state, to determine the ground state energy, the radius of the electron orbit and the electron speed.

(2)

(c)According to the Schrödinger model, the position and the speed of an electron are not well defined. It can be assumed that the uncertainty in the position of the electron in a hydrogen atom is equal to the radius of the electron orbit in the n = 1 state.

(i)Apply the Heisenberg uncertainty principle to hydrogen in this state to show that the uncertainty in the speed of the electron is approximately equal to the electron speed as calculated in (b).

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(3)

(ii)Explain why the result in (i) above suggests that the idea of electron orbits, as used in the Bohr model, is a poor one.

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(3)

(Total 10 marks)

11.This question is about the Bohr model of the hydrogen atom and the extension of the model to include singly ionized helium.

In his theory of the hydrogen atom, Bohr refers to stable electron orbits.

(a)State the Bohr postulate that determines which stable orbits are allowed.

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(1)

(b)Describe how the existence of such orbits accounts for the emission line spectrum of atomic hydrogen.

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(3)

The Bohr model of the hydrogen atom can be extended to singly ionized helium atoms. The model leads to the following expression for the energy En of the electron in an orbit specified by the integer n.

En=

where k is a constant.

In the spectrum of singly ionized helium, the line corresponding to a wavelength of 362 nm arises from electron transitions between the orbit n = 3 to the orbit n = 2.

(c)Deduce the value of the ionization energy of singly ionized helium atoms.

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(4)

(d)Outline how the Schrödinger model of the hydrogen atom leads to the idea of discrete electron energy levels.

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(2)