SME
Grade 12 Science · Problem type
How much mass the Sun turns into light
Use this for “The Sun gives off 3.828 × 10²⁶ W. How much mass does it turn into energy each second?”
Diagram
Mass numbers (top) and atomic numbers (bottom) add to the same on both sides.
A positron is a positive electron: a proton turned into a neutron.
Luminosity: 3.828 × 10²⁶ W
Mass turned to energy each second: 4.25 × 10⁹ kg/s
Hydrogen fused each second: 6.08 × 10¹¹ kg/s
This is an example. Type your own values to start a new problem.
m (kg/s)
=
L (W)
÷
(9.00
×
10¹⁶
m²/s²)
H
Hydrogen fused each second
calculated · kg/s
Formulas
m
=
L
9.00 ×
10
16
4.25 ×
10
9
=
3.828 ×
10
26
9.00 ×
10
16
H
=
m
0.007
6.08 ×
10
11
=
4.25 ×
10
9
0.007
Assumptions
•
0.7 % of the hydrogen’s mass becomes energy (E = mc²).
•
The Sun shines by this chain in its core: 4 ¹H → ⁴He + 2 e⁺ + 2 neutrinos.
•
c = 3.00 × 10⁸ m/s, so c² = 9.00 × 10¹⁶ m²/s².
Step-by-step
WE KNOW
L = 3.828 × 10²⁶ W
FIND
mass turned to energy each second (m), hydrogen fused each second (H)
Step 1 · Find mass turned to energy each second (m)
Use m = L ÷ (9.00 × 10¹⁶)
E
=
mc²:
each
second’s
energy
over
c
2
is
the
mass
it
came
from.
m
=
3.828 ×
10
26
9.00 ×
10
16
m
=
4.253 ×
10
9
kg/s
Step 2 · Find hydrogen fused each second (H)
Use H = m ÷ 0.007
The mass lost is only 0.7 % of the hydrogen fused.
H
=
4.253 ×
10
9
0.007
H
=
6.08 ×
10
11
kg/s
Check
Put the numbers back in. Both sides should match.
4.253 ×
10
9
≈
3.828 ×
10
26
9.00 ×
10
16
✓
6.08 ×
10
11
≈
4.253 ×
10
9
0.007
✓
← Previous lesson
The sun and stellar evolution: fusion, the H-R diagram, nucleosynthesis and black holes
Next lesson →
A star’s mass sets its life
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Refresh
Related lessons
The sun and stellar evolution: fusion, the H-R diagram, nucleosynthesis and black holes
Main lesson
A star’s mass sets its life
Use this for “A star has twice the Sun’s mass. How bright is it, and how long will it last?”
The life of a Sun-like star
Use this for “Put the stages of a Sun-like star’s life in order. What is left at the end?”
The life of a massive star
Use this for “What is left after a massive star explodes as a supernova?”
Where the atoms were made
Use this for “Which two elements are the most common in the universe, and where were they made?”