91影视

The energy released by 鈥減rotons and neutrons鈥� present in the nucleus is termed as nuclear energy.

This type of energy can be generated in one of two ways:

• Fission (when atom nuclei split into several pieces) or
• Fusion (when nuclei fuse together).

From Einstein's equation:

$螖E=m{c}^2$

wheremis the mass difference between reactants and products:

$螖m=m_{products}-m_{reac\tan ts}$

Binding energies are commonly expressed in millions of electron volts, that is, in mega-electron volts (MeV):

$1MeV={10}^{6}eV=1.602x{10}^{-13}J$

A particularly useful factor converts the atomic mass unit to its energy equivalent in electron volts:

$1amu=931.5x{10}^{6}eV=931.5MeV$

The change in mass when 1 Kg of antimatter annihilates 1 Kg matter:

$$\begin{gathered} 螖m=0-2kg=-2kg \\ 螖E=螖m{c}^2.....\left(i\right) \end{gathered}$$

The known values are substituted.

$$\begin{gathered} 螖E=(-2kg){\left(2.99792x{10}^8\frac{m}{s}\right)}^2\left(\frac{J}{\frac{kg路m^2}{s^2}}\right) \\ 螖E=-1.7975脳{10}^{17}J \end{gathered}$$

(Note: it is negative since the energy is being released)

b. Energy released per kilogram of antihydrogen.

$4_1^{1}H{鈫�}_2^{4}He+2_1^0尾$

$$\begin{gathered} 螖m=\left[4\right(1.007825amu\left)\right]-[4.0026amu+2(0.000549amu\left)\right] \\ =0.02760amu \end{gathered}$$

$$\begin{gathered} T_{螖m}=\left(1x{10}^5\right.Hatoms)\left(\frac{0.02760amu}{{}^{4}He}\right)\left(\frac{1{}^{4}He}{4Hatoms}\right) \\ {T}_{螖m}=6.9x{10}^{2}amu \end{gathered}$$

$$\begin{gathered} H_{anti}=1kg\left[\frac{1000g}{1kg}\right]\left[\frac{1mol}{1.008g}\right]\left[\frac{6.022x{10}^{23}antiH}{1molantiH}\right] \\ {H}_{anti}=5.9742脳{10}^{26}antiH \end{gathered}$$

$$\begin{gathered} E=6.9x{10}^{2}amu\left[\frac{931.5MeV}{1amu}\right]\left[\frac{1.602x{10}^{-16}kJ}{1MeV}\right] \\ =1.0297x{10}^{-10}kJ \end{gathered}$$

$$\begin{gathered} E_{released}=\left[\frac{1.0297脳{10}^{-10}kJ}{antiH}\right]\left[5.9742脳{10}^{26}\right.anti\left.H\right] \\ =6.151脳{10}^{16}kJ \end{gathered}$$

c. From the calculation with excess hydrogen, it is observed that procedure (b) produces more energy per kg of antihydrogen.