Question

The sun produces energy via fusion. One of the fusion reactions that occurs in the sun is 411H→42He+201e How much energy in joules is released by the fusion of 2.01 g of hydrogen-1? Express your answer to three significant figures and include the appropriate units.

Answer 1

Answer: The energy released for the the given amount of hydrogen -1 atom is $1.2474\times 10^{11}J$

Explanation:

First we have to calculate the mass defect $(\Delta m)$.

The given equation follows:

$4_{1}^{1}\textrm{H}\rightarrow _{2}^{4}\textrm{He}+2_0^{1}\textrm{e}$

To calculate the mass defect, we use the equation:

Mass defect = Sum of mass of product - Sum of mass of reactant

$\Delta m=(2m_{e}+m_{He})-(4m_{H})$

We know that:

$m_e=0.00054858g/mol\\m_{H}=1.00782g/mol\\m_{He}=4.00260g/mol$

Putting values in above equation, we get:

$\Delta m=((2\times 0.00054858)+4.00260)-(4\times 1.00782)=-0.027583g=-2.7583\times 10^{-5}kg$

(Conversion factor: 1 kg = 1000 g )

To calculate the energy released, we use Einstein equation, which is:

$E=\Delta mc^2$

$E=(-2.7583\times 10^{-5}kg)\times (3\times 10^8m/s)^2$

$E=-2.4825\times 10^{11}J$

The energy released for 4 moles of hydrogen atom is $2.4825\times 10^{11}J$

To calculate the number of moles, we use the equation:

$\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}$

Given mass of hydrogen atom = 2.01 g

Molar mass of hydrogen atom = 1 g/mol

Putting values in above equation, we get:

$\text{Moles of hydrogen atom}=\frac{2.01g}{1g/mol}=2.01mol$

We need to calculate the energy released for the fusion of given amount of hydrogen atom. By applying unitary method, we get:

As, 4 moles of hydrogen atom releases energy of = $2.4825\times 10^{11}J$

Then, 2.01 moles of hydrogen atom will release energy of = $\frac{2.4825\times 10^{11}}{4}\times 2.01=1.2474\times 10^{11}J$

Hence, the energy released for the the given amount of hydrogen -1 atom is $1.2474\times 10^{11}J$