Practice Paper 2 (HL IB Physics)

State and explain one piece of experimental evidence that supports the theory of special relativity.

Muons are unstable particles that are created in the Earth's upper atmosphere. Muons have an average half-life of 1.49 µs as measured from the reference frame where the muon is at rest. Muons travel at a speed of 0.987c towards the surface of the Earth relative to Earth. 

A detector positioned at 5196 m above the surface of the Earth detects muons at a rate of 3.2 × 10⁴ per hour.

A second detector is positioned at ground level.

Calculate the half-life of the muons as measured by an observer on Earth.

Calculate the distance between the detectors as measured from the reference frame of the muon.

The diagram represents a stationary wave formed on a violin string fixed at P and Q when it is plucked at its centre. X is a point on the string at maximum displacement.

Explain why a stationary wave is formed on the string.  

The stationary wave formed represents the "A" string of a violin which has a frequency of 440 Hz. 

Calculate the time taken for the string at point X to move from maximum displacement to its next maximum displacement.

The distance from the Earth to the Sun is 1.5 × 10¹¹ m. The mass of the Earth is 6 × 10²⁴ kg and the mass of the Sun is 3.3 × 10⁵  times the mass of the Earth.

Estimate the gravitational force between the Sun and the Earth.

Mars is 1.5 times further away from the Sun than the Earth and is 10 times lighter than Earth.

Predict the gravitational force between Mars and the Sun.

Determine the acceleration of free fall on a planet 20 times as massive as the Earth and with a radius 10 times larger.

Calculate the orbital speed of the Earth around the Sun.

A magnet is dropped through a vertical solenoid.

On the axes provided sketch a graph of the expected e.m.f. as time progresses.

Explain the shape of the graph from part (a).

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

The half−life of 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 and no atoms. At any given time, most of the atoms are either or with a negligible number of atoms in other forms in the decay series.

Sketch on the axes below the variation of number of atoms and the number of 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.

A certain time, t, after its formation, the sample contained twice as many atoms as atoms. 

Show that the number of atoms in the rock sample at time t was 4.0 × 10²².

The ratio of the number of lead nuclei to the number of uranium nuclei at some time t is given by: 

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

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

Lead−214 is an unstable isotope of lead−206. It decays by emitting a  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

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. 

The Sun emits radiation with a peak emission occurring at a wavelength of 5.2 × 10⁻⁷ m.

Show that the Sun has a surface temperature of about 6000 K.

The average intensity of radiation received from the Sun at the surface of the Earth is 1370 W m⁻². 

Show that the Sun's luminosity is about 4 × 10²⁶ W.

Mean distance between the Sun and the Earth = 1.49 × 10¹¹ m

Use the Stefan-Boltzmann law to determine the radius of the Sun.

An idealised refrigerator cycle is shown on the pressure-volume diagram below.

An experiment to determine the charge of an electron is shown.   

Oil drops are sprayed into a chamber above two parallel metal plates which are separated by a distance d. The oil drops become charged before entering the region between the plates.

A potential difference V is applied between the plates.

An oil drop is observed to be stationary between the plates when the potential difference is . When the potential difference is increased to , the drop is observed to move upwards with a constant velocity .

Draw the forces acting on the oil drop when and when .

Show that the electric charge on the oil drop is given by

where  is the viscosity of air and is the radius of the oil drop.

The following measurements are made for the oil drop:

The viscosity of air between the plates is  and the separation of the plates is .

Deduce, using the equation in part (c), whether the value of the charge for the oil drop is consistent with the currently accepted value of the elementary charge.

The voltage supply connected to the parallel plates is switched off. The oil drop falls with a constant velocity .

Show that  is about 0.2.

The oil drop collides with another oil drop of charge +14e, where e is the elementary charge.

Deduce the net charge on each oil drop after the collision.

The Bohr model was developed in order to explain the atomic spectrum of hydrogen.

Outline the Bohr model and give a limitation of it.

Bohr modified the Rutherford model by introducing the condition: 

. 

Outline the reason for this modification.

The Bohr model for hydrogen can also be applied to a helium atom which has lost one of its electrons through ionisation.

The one remaining electron has a mass of m and moves in a circular orbit of radius r. Deduce an expression for

the kinetic energy of the electron

the electric potential energy

the total energy of the atom

Using your answer to (c), describe the predicted effect on the orbital radius of the electron when it

The radius of the electron's orbit in the helium atom is 2.43 × 10⁻¹⁰ m.

Determine the principal quantum number of the energy level occupied by the electron.

The total energy of an electron in a stable orbit of a hydrogen atom is given by:

State and explain what physical quantity is represented by the constant K.

In 1908, the physicist Friedrich Paschen first observed the photon emissions resulting from transitions from a level n to the level n = 3 of hydrogen and deduced their wavelengths were given by:

where A is a constant.

Justify this formula on the basis of the Bohr theory for hydrogen and determine an expression for the constant A.