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Date	May 2017	Marks available	1	Reference code	17M.3.HL.TZ2.7
Level	Higher level	Paper	Paper 3	Time zone	2
Command term	Show that	Question number	7	Adapted from	N/A

Question

State what is meant by the event horizon of a black hole.

[1]

a.i.

Show that the surface area A of the sphere corresponding to the event horizon is given by

$A = \frac{{16\pi {G^2}{M^2}}}{{{c^4}}}$ .

[1]

a.ii.

Suggest why the surface area of the event horizon can never decrease.

[1]

a.iii.

The diagram shows a box that is falling freely in the gravitational field of a planet.

A photon of frequency f is emitted from the floor of the box and is received at the ceiling. State and explain the frequency of the photon measured at the ceiling.

[3]

Markscheme

the surface at which the escape speed is the speed for light
OR
the surface from which nothing/not even light can escape to the outside
OR
the surface of a sphere whose radius is the Schwarzschild radius

Accept distance as alternative to surface.

[1 mark]

a.i.

use of $A = 4\pi {R^2}$ and $R = \frac{{2GM}}{{{c^2}}}$