10^6 mathrm(Tha)=(2)/(3) cdot 2,7 cdot 10^25 mathrm(u)^-3 mathrm(E)

To solve the equation \( 10^{6} \mathrm{Tha} = \frac{2}{3} \cdot 2.7 \cdot 10^{25} \mathrm{u}^{-3} \mathrm{E} \), we need to understand the units involved and perform the necessary conversions.<br /><br />1. **Tha (Teraton)**: 1 Teraton (Tha) = \( 10^{12} \) grams (g).<br /><br />2. **u (atomic mass unit)**: 1 atomic mass unit (u) = \( 1.66053907 \times 10^{-24} \) grams (g).<br /><br />3. **E (electronvolt)**: 1 electronvolt (eV) = \( 1.60218 \times 10^{-19} \) joules (J).<br /><br />Let's break down the right-hand side of the equation:<br /><br />\[ \frac{2}{3} \cdot 2.7 \cdot 10^{25} \mathrm{u}^{-3} \mathrm{E} \]<br /><br />First, convert \( \mathrm{u}^{-3} \) to grams:<br /><br />\[ \mathrm{u}^{-3} = \left( 1.66053907 \times 10^{-24} \mathrm{g} \right)^{-3} = 8.9875 \times 10^{-23} \mathrm{g}^{-3} \]<br /><br />Now, multiply this by 2.7 and \( 10^{25} \):<br /><br />\[ 2.7 \cdot 10^{25} \cdot 8.9875 \times 10^{-23} \mathrm{g}^{-3} = 2.7 \cdot 8.9875 \cdot 10^{2} \mathrm{g}^{-3} = 24.5 \cdot 10^{2} \mathrm{g}^{-3} = 2.45 \times 10^{3} \mathrm{g}^{-3} \]<br /><br />Now, multiply by \( \frac{2}{3} \):<br /><br />\[ \frac{2}{3} \cdot 2.45 \times 10^{3} \mathrm{g}^{-3} = 1.6333 \times 10^{3} \mathrm{g}^{-3} \]<br /><br />Next, convert this to electronvolts (eV):<br /><br />\[ 1.6333 \times 10^{3} \mathrm{g}^{-3} \times \left( \frac{1 \mathrm{J}}{1.60218 \times 10^{-19} \mathrm{g}} \right) \times \left( \frac{1 \mathrm{eV}}{1.60218 \times 10^{-19} \mathrm{J}} \right) = 1.022 \times 10^{8} \mathrm{eV} \]<br /><br />Now, we have:<br /><br />\[ 10^{6} \mathrm{Tha} = 1.022 \times 10^{8} \mathrm{eV} \]<br /><br />Since 1 Teraton (Tha) = \( 10^{12} \) grams (g), we need to convert grams to electronvolts:<br /><br />\[ 10^{6} \mathrm{Tha} = 10^{6} \cdot 10^{12} \mathrm{g} = 10^{18} \mathrm{g} \]<br /><br />Convert grams to electronvolts:<br /><br />\[ 10^{18} \mathrm{g} \times \left( \frac{1 \mathrm{eV}}{1.66053907 \times 10^{-24} \mathrm{g}} \right) = 6.022 \times 10^{21} \mathrm{eV} \]<br /><br />So, the equation becomes:<br /><br />\[ 6.022 \times 10^{21} \mathrm{eV} = 1.022 \times 10^{8} \mathrm{eV} \]<br /><br />This is not possible, indicating a mistake in the initial setup or conversion steps. Please verify the units and constants used.