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Question 18N.3.HL.TZ0.18

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Date November 2018 Marks available [Maximum mark: 11] Reference code 18N.3.HL.TZ0.18
Level HL Paper 3 Time zone TZ0
Command term Calculate, Describe, Determine, Draw, Show that Question number 18 Adapted from N/A
18.
[Maximum mark: 11]
18N.3.HL.TZ0.18

The surface temperature of the star Epsilon Indi is 4600 K.

(a.i)

Determine the peak wavelength of the radiation emitted by Epsilon Indi.

[1]

Markscheme

λ = « 2.9 × 10 − 3 4600 =» 630 «nm» ✔

(a.ii)

Using the axis, draw the variation with wavelength of the intensity of the radiation emitted by Epsilon Indi.

[2]

Markscheme

black body curve shape ✔

peaked at a value from range 600 to 660 nm ✔

(a.iii)

The following data are available for the Sun.

Surface temperature  = 5800 K

Luminosity                  = L ⊙

Mass                          = M ⊙

Radius                       = R ⊙

Epsilon Indi has a radius of 0.73  R ⊙ . Show that the luminosity of Epsilon Indi is 0.2  L ⊙ .

[2]

Markscheme

L L ⊙ = ( 0.73 R ⊙ R ⊙ ) 2 × ( 4600 5800 ) 4 ✔

L = 0.211  L ⊙ ✔

(b)

Epsilon Indi is a main sequence star. Show that the mass of Epsilon Indi is 0.64  M ⊙ .

 

[1]

Markscheme

M = « 0.21 1 3.5 M ⊙ =» 0.640  M ⊙ ✔

(c)

The Sun will spend about nine billion years on the main sequence. Calculate how long Epsilon Indi will spend on the main sequence.

 

[2]

Markscheme

T E T ⊙ = « M E L E M ⊙ L ⊙ = 0.64 0.21 = » 3.0  ✔

T ≈ 27 billion years ✔

(d)

Describe the stages in the evolution of Epsilon Indi from the point when it leaves the main sequence until its final stable state.

[3]

Markscheme

red giant ✔

planetary nebula ✔

white dwarf ✔

 

do NOT accept supernova, red supergiant, neutron star or black hole as stages

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