Markscheme for questions on Cosmology

1.       any 4 from:
end of H burning/red giant/supergiant (1)
onset of He fusion/fusion of heavier nuclei (1)
gravitational collapse of core (1)
supernova explosion/ star explodes (1)
suitable mass limit (chanderasekha limit 1.4M) (1)
supported against gavity by neutron gas pressure/ ref to
Fermi pressure (1)
internal structure protons and electrons combined/ very
thin atmosphere/ metallic crust (1)                                                                             4

[4]

  2.     Any 5 from
red shift data for galaxies (accept stars)                                                                     1
calculate velocity from red shift                                                                                1
galaxies/ stars receding from Earth                                                                             1
distance data for galaxies/ stars                                                                                  1
velocity α distance / v/r = constant / v-r graph straight line                                         1
universe began at a single point                                                                                 1

[5]

  3.     (a)     Any two
stars rotate around galactic centre                                                                     1
star with velocity component towards Earth                                                     1
reference to motion/shape of galaxy                                                                1
or other valid points eg blue shift

  (b)   Ho = 75/ 3 × 1019 s–1                                                                                        1
t ≈ 1/ 2.5 × 10–18                                                                                              1
t ≈ 4 × 1017 s                                                                                                    1

[5]

  4.     Hydrogen atoms/particles (1)
Collapse under gravity/ decrease of gpe (1)
Increase in kinetic energy/ temperature (1)
Fusion of protons (1)
Energy released/ ref. to E = ∆mc2 (1)

[5]

5.       Any 6 from
Nuclear/hydrogen burning ends (1)

          Mass > Chandrasekhar limit (1)

          Expanding gas/planetary nebular/red giant (1)

          Gravitational collapse /ref. to burning He or higher metals (1)

          Correct ref. to (Fermi) pressure/ radiation pressure (1)
(must have ref. to pressure or force from radiation.)

          Neutron star (neutron by itself, not enough) (1)

          Correct reference to Schwarzschild radius/
allow mass> 3M/ allow ref. critical radius (1)

          Black Hole (1)                                                                                                           6

[6]

  6.     Ho2 = (1 × 10–26 × 8 × π × 6.67 × 10–11) / 3                                                             C1
Ho = 2.36 × 10–18 s–1                                                                                              A1

[2]

  7.     (i)      v/c = ∆λ / λ (1)
∆λ = 656.3 × 10–9 × 6.1 / 3 × 108 (ignore minus sign) (1)
∆λ = 1.33 × 10–14 m (1)                                                                                    3

  (ii)   Graph: any 4 points plotted correctly (1)
all correct (1)                                                                                                    2

  (iii)  graph: draw curve, reasonable attempt (1)                                                        1

(iv)    Either point where star moves perpendicular to line of sight (1)                       1

  (v)   time = 72 h ± (1)h (ecf read value from their graph ± 1 h) (1)                          1

  (vi)  r = 3√(6.7 × 10–11 × 4 × 1030 × [72 × 3600]2/ 4π2) ecf (1)
r = 7.70 × 109 m ecf . (1)                                                                                  2
(use of t = 72h 1/2)

[10]

Doppler Shift

8

a Which transition

Use of (

Δ)E = hc/λ OR (Δ)E = hf and f = c/λ 1

Use of 1.6 x 10

-19 1

Correct answer [1.9 eV]

1

C to B / -1.5 to – 3.4

1 4

[Accept reverse calculations to find wavelengths]

e.g.

(6.63 x 10

-34 J s)(3.00 x 108 m s-1)/

(656 x 10

-9 m)(1.6 x 10-19 J eV-1)

= 1.9 eV

b Explanation of absorption line

QOWC

1

Light of this wavelength is absorbed by hydrogen

1

In the outer part of the Sun (OR Sun’s atmosphere)

1

Absorbed radiation is reemitted in all directions

1

Transition from B to C (OR -3.4 to -1.5)

1 Max 4

c i Why galaxy receding

Wavelength increased (OR stretched) / red shift /

frequency decreased

1

c ii Calculation of speed

Use of

v/c = Δλ/λ 1

Correct answer [1.78 x 10

7 m s-1] 1 3

e.g.

(3.00 x 10

8 m s-1)(695 x 10-9 m – 656 x 10-9 m)/

(656 x 10

-9 m)

= 1.78 x 10

7 m s-1

[N.B. Use of wrong wavelength in denominator gives

1.68 x 10

7]

OR

Use of

v = fλ and v/c = Δf/f 1

Correct answer [1.67 x 10

7 m s-1] 1

[Look for

(4.573 x 10

14 Hz – 4.317 x 1014 Hz) / (4.537 x 1014 Hz)

N.B. Use of wrong frequency in denominator gives 1.78

x 10

7]

Total 11

Questions on resistivity

Resistivity

1. A coil of constantan wire of length 2 m has an area of cross-section of

7 x 10^-7 m². If its resistivity is 49 x 10^-8 Ω m, find its resistance.

2. A coil of wire 4 m long has a resistance of 20 Ω. If its resistivity is

108 x 10^-8 Ω m, find its area of cross-section.

3. A 1.75 m length of tin wire with a diameter of 0.70 mm is found to have a resistance of 0.5 Ω Find the resistivity of tin.

4. A resistor of 2 Ω is to be made from manganin wire of resistivity

42 x 10^-8 Ω m having a diameter of 0.42 mm. What length is required?

5. Find the resistance of a wire 2.8 m long with a resistivity of 22 x 10^-8 Ω m and a diameter of 0.56 mm.
6. A wire has a resistance of 2 Ω Find the resistance of a wire of the same material which is three times as long, but with half the diameter.

 

Mark Scheme February assessment

1.       The sum of the currents entering a point / junction is equal to the sum of the currents

leaving (the same point) Or ‘Algebraic sum of currents at a point = 0’                    B2

(–1 for the omission of ‘sum’ and -1 for omission of ‘point’/ ‘junction’)

(Do not allow I1 + I2 = I3 + I4 unless fully explained)

[2]

  2.     A:   gamma / γ (ray/radiation/wave)                                                                        B1
       λ = 10–16 to 10–10 (m)                                                                                       B1
B:    infrared / IR / i.r.                                                                                              B1
       λ = 7 × 10–7 to 10–3 (m)                                                                                    B1

[4]

  3.     (i)      v   = I / nAe = 0.0025 / (8.5 × 1028 × 1.1 × 10–7 × 1.6 × 10–19) (1)
     = 1.67 × 10–6 m s–1 (1)                                                                                2

  (ii)   Free electron concentration (or wtte) is much smaller in the thermistor than
in the wire.                                                                                                       1

[3]

  4.     (a)     R = R1 + R2 / R = 200 + 120 / R = 320                                                            C1
current =                                                                                                 C1
current = 2.5 ´ 10–2 (A)                                                                                 A0

  (b)   V = 25 ´ 10–3 ´ 120 / V =
V = 3.0 (V)                (Possible ecf)                                                                B1

  (c)   p.d. across the 360 (W) resistor = p.d. across the 120 (W) resistor /
There is no current between A and B / in the voltmeter                                 B1
(Allow ‘A & B have same voltage’ - BOD)

          The p.d. calculated across 360 W resistor is shown to be 3.0 V /
The ratio of the resistances of the resistors is shown to be the same.             B1

[5]

  5.     (i)      plane polarised light vibrates (travels) in one plane only                                B1
(look for reference to one plane of oscillation)

(ii)     only transverse waves can be polarised/AW                                                  B1
sound waves are longitudinal/not transverse/AW                                           B1

[3]

6.       (a)     (i)      amplitude = 3.75 cm {allow 3.7 to 3.8)                                                B1

(ii)     when t = 1.8 ms displacement = ANY negative value                           B1

(–)3.35 cm (ALLOW 3.3 TO 3.4)                                                         B1

(iii)    period = 2.64 ms (allow 2.64 to 2.68)                                                   B1

(iv)    frequency = 1/period                                                                            C1

= 1/(2.64 × 10 – 3) = 379 Hz (379 to 373 or 380) {ecf for T}              A1

  (b)   recall of v = fl                                                                                               C1

l = v/f = 300/379 = 0.79 m (or 0.8 m) {allow ecf from (iv)}                         A1

[8]

  7.     Any three properties from:                  (–1 for each error or contradiction)        B1 ´ 3

1.      Travel at the speed of light / c / 3 ´ 108 m s–1 (NOT ‘same speed’)

2.      Travel through vacuum / ‘free space’

3.      Have oscillating electric and magnetic fields

4.      They are (all) transverse waves / can be polarised

5.      Allow: ‘They show diffraction / reflection / refraction / interference’

6.      Allow: ‘Consist of photons’

Any three regions from the list below:                                                               B1 ´ 3

Gamma (rays / radiation) / g (rays) ; X-rays ; u.v ; ir ; microwaves ; radio waves

(NOT ‘radio’)

One suitable application for the opted region.                                                         B1

(E.g.: Gamma rays for radiotherapy / sterilisation;

X-rays for taking pictures of skeleton / bones; u.v for tanning; ir for TV remote
control; microwaves for cooking / mobile phones; radio waves for communication)

(Note: Reference to alpha, beta and gamma can only score the last marking point)

[7]

  8.     (i)      evidence of knowledge of:
full/max transmission when the (transmission axis of) polarising sheet is
parallel to the light’s plane of polarisation/vibrations                                     B1
no transmission when the (transmission axis of) polarising sheet is at right
angles to light’s plane of polarisation/vibrations                                            B1

(ii)     reflected light from surface is partially plane polarised                                  B1
polarising sheet is placed at right angles to reflected light’s polarisation        B1
plane/AW

[4]

  9.       (b)                                                    (Allow other subject, with or without D)     C1
(charge =) 7800 ´ 0.23                                                                                            C1
1.794 ´ 103 » 1.8 ´ 103 (C)                                                  (Ignore minus sign)     A1
(1.8 ´ 106 (C) scores 2/3)

(c)     (number =)           (Possible ecf)                                                    C1
(number =) 1.12 ´ 1022 » 1.1 ´ 1022                                                              A1

[6]

Answers to questions on probing the nucelus

Y13 Answers on capacitance

markscheme (projectiles & moments)

Charge and Discharge of Capacitors

2 a) 470 s
b) 564 uF
c) 3.8 uC
d) 0.081V

3 a) 600 uC
b) 1.8 mJ
c) 2 s
d) 10 s

4 a) 90 uC
b) 7.5 s
c) 6.0 V
d) 12 uA
e) 7.5 s

5 1.39 s

6 a) 0.90 uC
b) 0.50 uC
c) 5.0 V
d) 4.0 V
e) 1.8 uA

7 120 ohms

y12 mock

Boyle's Law

Note. Any convenient units can be used for pressure and volume, provided that the units for P₁ are the same as those for P₂, and that the units for V₁ are the same as those for V₂.

(Use g = 9.8 N kg^-1)     1 atm =  Atmospheric pressure = 100 000 Pa = 100 000 Nm^-2

1. A fixed mass of gas at constant temperature has a volume of 500 cm² at a pressure of 1 atm. What will its volume be at a pressure of 4 atm?  125 cm³

2. A gas has a volume of 600cm³ at a pressure of 3.0 x 10⁵ Pa.  What is its volume at a pressure of 6.0 x 10⁵ Pa?  300 cm³

3. A gas has a volume of 1000 cm³ at a pressure of 1 atm. At what pressure will it occupy 100 cm³?   10 atm

4. The pressure exerted by a gas is due to the molecules of the gas bombarding the walls of the container. Why does the pressure increase when the volume is decreased at constant temperature? Less volume, molecules closer together, more collisions etc

5. A cylinder of compressed air has a volume of 51 cm³ at a pressure of 8 atm. When the cylinder is opened, what volume of air will escape?                                           

P₁V₁ = P₂V₂

rearranging V₂ = P₁V₁/ P₂           

V₂ = 8 x 51/ 1 = 408 cm³ minus the 51cm³ left in the cylinder = 357 cm³

 

6. A diver is working in sea-water of density 1025 kg m^-3 on a day when atmospheric pressure is 100 450 Pa. A bubble from his mask is three times the volume when it reaches the surface. At what depth is he working? 20m

7. A lake is 92.7 m deep. A bubble at the bottom of the lake has a volume of 0.5 cm³. What will its volume be at the surface if a water barometer would read 10.3 m (i.e. atmospheric pressure is the same as the pressure at this depth)? 5cm³

8. A uniform cylinder 0.60 m long is sealed at one end. It is lowered open end downwards into a lake so that the mouth just touches the bottom. When retrieved the inside is wet up to 0.50 m from the mouth. Find the depth of the lake if a water barometer would read 10.4 m of water. 52.5m

9. A cylindrical diving bell 8 m high is lowered into water so that the top of the bell is 0.75 m below the surface. If the atmospheric pressure is the same as that exerted by a column of water 10.25 m high, find how far the water rises inside the bell. 6m

A vessel of volume 500 cm³ containing air at a pressure of 8.0 x 10⁴ Pa is connected by a very narrow tube fitted with a tap, to a vessel of volume 700 cm³ containing air at a pressure of 2.0 x 10⁵ Pa. What is the resulting pressure in the vessels when the tap is opened?                     1.5 x10⁵ Pa

A compression pump is connected to a vessel of volume 500 cm³. For each stroke of the pump the piston sweeps 50 cm³ of air at atmospheric pressure into the vessel. If the initial pressure in the vessel is 1 atm, find the pressure in the vessel after 2 strokes.

1.2 atm

An exhaust pump is connected to a flask of volume 100 cm³. The volume swept out by the piston is 25 cm³ for each stroke. The pressure in the vessel is originally 1 atm. By considering one stroke at a time, find the pressure in the vessel after two strokes. 0.64atm