Respuesta :
Answer: The energy released for the the given amount of hydrogen -1 atom is [tex]1.2474\times 10^{11}J[/tex]
Explanation:
First we have to calculate the mass defect [tex](\Delta m)[/tex].
The given equation follows:
[tex]4_{1}^{1}\textrm{H}\rightarrow _{2}^{4}\textrm{He}+2_0^{1}\textrm{e}[/tex]
To calculate the mass defect, we use the equation:
Mass defect = Sum of mass of product - Sum of mass of reactant
[tex]\Delta m=(2m_{e}+m_{He})-(4m_{H})[/tex]
We know that:
[tex]m_e=0.00054858g/mol\\m_{H}=1.00782g/mol\\m_{He}=4.00260g/mol[/tex]
Putting values in above equation, we get:
[tex]\Delta m=((2\times 0.00054858)+4.00260)-(4\times 1.00782)=-0.027583g=-2.7583\times 10^{-5}kg[/tex]
(Conversion factor: 1 kg = 1000 g )
To calculate the energy released, we use Einstein equation, which is:
[tex]E=\Delta mc^2[/tex]
[tex]E=(-2.7583\times 10^{-5}kg)\times (3\times 10^8m/s)^2[/tex]
[tex]E=-2.4825\times 10^{11}J[/tex]
The energy released for 4 moles of hydrogen atom is [tex]2.4825\times 10^{11}J[/tex]
To calculate the number of moles, we use the equation:
[tex]\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}[/tex]
Given mass of hydrogen atom = 2.01 g
Molar mass of hydrogen atom = 1 g/mol
Putting values in above equation, we get:
[tex]\text{Moles of hydrogen atom}=\frac{2.01g}{1g/mol}=2.01mol[/tex]
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 = [tex]2.4825\times 10^{11}J[/tex]
Then, 2.01 moles of hydrogen atom will release energy of = [tex]\frac{2.4825\times 10^{11}}{4}\times 2.01=1.2474\times 10^{11}J[/tex]
Hence, the energy released for the the given amount of hydrogen -1 atom is [tex]1.2474\times 10^{11}J[/tex]
