Question 23M.3.HL.TZ1.19
| Date | May 2023 | Marks available | [Maximum mark: 7] | Reference code | 23M.3.HL.TZ1.19 |
| Level | HL | Paper | 3 | Time zone | TZ1 |
| Command term | Estimate, Show that, State, Suggest | Question number | 19 | Adapted from | N/A |
A spherical nebula has radius 9 × 1015 m and contains 1010 atoms of hydrogen per cubic metre. Show that the mass of the nebula is about 5 × 1031 kg.
[2]
V = «= = 3.05 × 1048 m3» ✓
M = 3.05 × 1048 × 1010 × 1.67 × 10−27 = 5.1 × 1031 «kg» ✓
For MP2, values must be substituted to show working.
Collapsed nebula. The calculation of the mass of a sphere of a given radius and density was done well. Also, students worked well with the concept of Jeans mass.
The Jeans mass MJ, in kg, for a nebula containing hydrogen at a Kelvin temperature T is given by
The nebula in (a) has a temperature of 50 K. Suggest why this nebula will not collapse to form a star.
[2]
« =» 6.4 × 1032 kg ✓
according to the Jeans criterion collapse will start when the mass of the star is greater than the Jeans mass✓
«which is not the case here»
The temperature of the nebula is decreasing. Estimate the temperature at which the nebula will begin to collapse.
[2]
= 5.1 × 1031 ✓
T ≈ 9 K ✓
State one condition for the collapsed nebula in (c)(i) to form a star.
[1]
the temperature at the core must be high enough for fusion «of hydrogen» to take place ✓
The mass of the Sun is 2 × 1030 kg and the Sun will spend 8 × 109 years on the main sequence. The collapsed nebula in (c) also becomes a main sequence star. Estimate the time this star will spend on the main sequence.
✓
✓
t = × 8 × 109 = 2.6 × 106 years ✓
Award [3] for correct alternative solution OR BCA from interval 2.2 to 2.8.
In d), only the best students correctly calculated the time the star would spend on the main sequence.