# Math Help - Math/Science twist

1. ## Math/Science twist

I found this question a bit confusing. Anyone who can help out with these answers.Your help is appreciated

In a main sequence star such as our Sun, a fusion reaction is ongoing that releases energy: the
pp chain, in which four hydrogen-1 nuclei (single protons) become one helium nucleus (alpha
particle). The resulting mass is less than the initial mass: this ‘mass loss’ is the source of Sun’s
energy which can be calculated from the equation: E= m*c
2 , where E is the energy released;
m is the ‘missing’ mass; and c is the speed of light,
3.0 * 105 km/s. The mass of one proton is
1.008 a.m.u (atoms mass unit: the mass of a carbon-12 nucleus is defined to be 12 a..m.u). The
mass of a helium-4 nucleus is 4.003 a.m.u: there is a deficit. 1 a.m.u = 1.66*10
-27 kg and it is
estimated that 3.6
×1038 protons are converted into helium nuclei every second.

A. What is the energy released in a single reaction where four protons ->
one He nucleus?

B. What is the power output of Sun? (3 marks)
Power = (number of reactions per second) X (energy released per reaction)

2. Originally Posted by srr2612
I found this question a bit confusing. Anyone who can help out with these answers.Your help is appreciated

In a main sequence star such as our Sun, a fusion reaction is ongoing that releases energy: the
pp chain, in which four hydrogen-1 nuclei (single protons) become one helium nucleus (alpha
particle). The resulting mass is less than the initial mass: this ‘mass loss’ is the source of Sun’s
energy which can be calculated from the equation: E= m*c
2 , where E is the energy released;
m is the ‘missing’ mass; and c is the speed of light,
3.0 * 105 km/s. The mass of one proton is
1.008 a.m.u (atoms mass unit: the mass of a carbon-12 nucleus is defined to be 12 a..m.u). The
mass of a helium-4 nucleus is 4.003 a.m.u: there is a deficit. 1 a.m.u = 1.66*10
-27 kg and it is
estimated that 3.6
×1038 protons are converted into helium nuclei every second.

A. What is the energy released in a single reaction where four protons ->
one He nucleus?

B. What is the power output of Sun? (3 marks)
Power = (number of reactions per second) X (energy released per reaction)

Something like the following:

Given: Mass of Hydrogen-1= 1.008 amu, mass of Helium-4=4.003 amu, four hydrogen-1 become one helium-4, speed of light = $3.0(10^5)km/s$ (we'll need this in m/s so converting $3.0(10^8)m/s$), and $1 amu= 1.66(10^{-27})kg$.

Take 4 times the mass of hydrogen, 4.032 amu, and subtract from it the helium mass, 4.003 amu, to get $\Delta m=0.029amu$ this is also our missing mass to soon be used after we convert to kg.

$\Delta m=0.029 amu|\frac{1.66(10^{-27})kg}{1 amu}$
After multiplying across and canceling the amu we're free to use $E=mc^2$

$c^2 = (3.0(10^8)m/s)^2 = 9.0(10^16)m^2/s^2$

$E = (4.814^{-29}kg)(9.0(10^{16})m^2/s^2) = 4.3326(10^{-12})J$

A) Keeping significant digits the energy is about $4.3(10^{-12})J$

for the second question we need to know how many helium are formed per second and we are given that $3.6(10^{38})p^{+}$ are converted to helium every second so divide that number by four, the number of proton it takes to create one helium, $9(10^{37})$ reactions per second.

Power = (number of reactions per second) X (energy released per reaction)
Power = $9(10^{37})He/s$ X $4.3326(10^{-12})J$
Power = $3.89934(10^{26})J/s$

B) Power of the sun is about $3.9(10^{26})J/s$