DP Physics (last assessment 2024)

Question 17N.3.HL.TZ0.20

20.

[Maximum mark: 10]

17N.3.HL.TZ0.20

(a)

The Sun is a second generation star. Outline, with reference to the Jeans criterion (M_J), how the Sun is likely to have been formed.

[4]

Markscheme

interstellar gas/dust «from earlier supernova»

gravitational attraction between particles

if the mass is greater than the Jean’s mass/M_j the interstellar gas coalesces

as gas collapses temperature increases leading to nuclear fusion

MP3 can be expressed in terms of potential and kinetic energy

(b)

Suggest how fluctuations in the cosmic microwave background (CMB) radiation are linked to the observation that galaxies collide.

[3]

Markscheme

fluctuations in CMB due to differences in temperature/mass/density

during the inflationary period/epoch/early universe

leading to the formation of galaxies/stars/structures

gravitational interaction between galaxies can lead to collision

[Max 3 Marks]

(c)

Show that the critical density of the universe is

$\frac{{3{H^2}}}{{8\pi G}}$

where H is the Hubble parameter and G is the gravitational constant.

[3]

Markscheme

ALTERNATIVE 1

kinetic energy of galaxy $\frac{1}{2}$ mv² = $\frac{1}{2}$ mH²r² «uses Hubble’s law»

potential energy = $\frac{{GMm}}{r}$ = G $\frac{4}{3}$ $\pi$ r³ $\rho \frac{m}{r}$ «introduces density»

KE=PE to get expression for critical $\rho$

ALTERNATIVE 2

escape velocity of distant galaxy v = $\sqrt {\frac{{2GM}}{r}}$

where H₀r = $\sqrt {\frac{{2GM}}{r}}$

substitutes M = $\frac{4}{3}$ $\pi$ r³ $\rho$ to get result

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