PHYSICS 7408/1 Paper 1

Section A
Answer all questions in this section.

01  An isotope of potassium 40K is used to date rocks. The isotope decays into an
isotope of argon (Ar) mainly by electron capture.

01.1  The decay is represented by this equation:

Complete the equation to show the decay by filling in the gaps.

[math]{}^{40}_{19}\mathrm{K} + {}^{0}_{-1}e \rightarrow \_\_  \mathrm{Ar} + \_\_ [/math]

Explanation:

[math]{}^{40}_{19}\mathrm{K} + {}^{0}_{-1}e \rightarrow {}^{\underline{40}}_{\underline{18}}\mathrm{Ar} +  \underline{{}^{0}_{0}\mathrm{ve}}[/math]

Through electron captured a proton is converted into neutron. So proton number goes down but nucleon number stays same. For conservation of lepton number electron neutrino will be produced.

[2 marks]

01.2 Explain which fundamental interaction is responsible for the decay in question 01.1.

[2 marks]

01.3 One decay mechanism for the decay of 40K results in the argon nucleus having an excess energy of 1.46 MeV. It loses this energy by emitting a single gamma photon.

Calculate the wavelength of the photon released by the argon nucleus.

[3 marks]

wavelength = [math]  \underline{ \, \, 8.51 \times 10^{13} \, \, } m[/math]

01.4 The potassium isotope can also decay by a second decay process to form a calcium-40 nuclide ([math]{}^{40}_{20}\mathrm{Ca}[/math]).
Suggest how the emissions from a nucleus of decaying potassium can be used to confirm which decay process is occurring.

[3 marks]

02  Figure 1 shows an arrangement used by a student to investigate vibrations in a stretched nylon string of fixed length l. He measures how the frequency f of first-harmonic vibrations for the string varies with the mass m suspended from it.

Figure 1

Table 1 shows the results of the experiment.

Table 1

02.1 Show that the data in Table 1 are consistent with the relationship

[math] f ∝ \sqrt{T}[/math]

where T is the tension in the nylon string.

02.2 The nylon string used has a density of 1150 kg m–3 and a uniform diameter of [math]5.0 × 10^{-4} m[/math].
Determine the length l of the string used.

[3 marks]

Explanation: 

l = ___________ m

02.3 The student uses the relationship in question 02.1 to predict frequencies for tensions that are much larger than those used in the original experiment.

Explain how the actual frequencies produced would be different from those that the student predicts.

[2 marks] 

Stretching the string will decrease its diameter, decreasing its mass per unit length causing its frequency to increase.

03  Figure 2 shows a ray of monochromatic green light incident normally on the curved surface of a semicircular glass block.

Figure 2 

03.1  The angle of refraction of the ray at the plane surface is 90°.

Refractive index of the glass used = 1.6

Calculate the angle of incidence of the ray on the flat surface of the block.

[1 mark]

angle of incidence = _______________  degrees

03.2  A thin film of liquid is placed on the flat surface of the glass block as shown in Figure 3.

Figure 3

The angle of incidence is changed so that the angle of refraction of the green light
ray at the glass–liquid interface is again 90°. The angle of incidence is now 58°.

Calculate the refractive index of the liquid.

[2 marks]

refractive index = _____________

03.3  The source of green light is changed for one that contains only red and blue light. For any material red light has a lower refractive index than green light, and blue light has a higher refractive index than green light. The angle of incidence at the glass–liquid interface remains at 58°.

Describe and explain the paths followed by the red and blue rays immediately after the light is incident on the glass–liquid interface.

[3 marks] 

As blue has a higher refractive index which makes its critical angle smaller than green so the angle of incidence will be greater than its critical angle and it will be totally internally reflected.

As red has a lower refractive index which makes its critical angle larger than green the angle of incidence will be less than its critical angle and it will be refracted by bending towards the normal.

04 An engineer wants to use solar cells to provide energy for a filament lamp in a road sign.

The engineer first investigates the emf and internal resistance of a solar cell under typical operating conditions.

The engineer determines how the potential difference across the solar cell varies with current. The results are shown in the graph in Figure 4.

The engineer uses the graph to deduce that when operating in typical conditions a single solar cell produces an emf of 0.70 V and has an internal resistance of 8.0 Ω.

04.1 Explain how the engineer uses the graph to obtain the values for the emf and internal resistance of the solar cell.

[2 marks]

EMF is obtained from y – intercept and internal resistance is the gradient on x -1 .

To operate effectively the lamp in the road sign needs a minimum current of 75 mA. At this current the resistance of the filament lamp is 6.0 Ω.

The engineer proposes to try the two circuits shown in Figure 5 and Figure 6.

Figure 6

04.2 Deduce, using calculations, whether the circuits in Figure 5 and Figure 6 are suitable for this application.

[4 marks]

04.3 Solar cells convert solar energy to useful electrical energy in the road sign with an efficiency of 4.0%.

The solar-cell supply used by the engineer has a total surface area of [math]32 cm^2[/math].

Calculate the minimum intensity, in [math]W m^{-2}[/math], of the sunlight needed to provide the minimum current of 75 mA to the road sign when it has a resistance of 6.0 Ω.

[3 marks]

intensity = _________________[math]W m^{-2}[/math]