Questions: 0.19900718 amu / 1 atom 235 U × 1.6606 × 10^-27 kg / 1 amu × (2.9979 × 10^8 m / 1 s)^2 × 6.022 × 10^23 atom 235 U / 1 mol 235 U × 1 J s^2 / 1 kg m^2 × 1 kJ / 1 × 10^3 J =

Transcript text: $\frac{0.19900718 \mathrm{amu}}{1 \mathrm{atom}{ }^{235} \mathrm{U}} \times \frac{1.6606 \times 10^{-27} \mathrm{~kg}}{1 \mathrm{amu}} \times\left(\frac{2.9979 \times 10^{8} \mathrm{~m}}{1 \mathrm{~s}}\right)^{2} \times \frac{6.022 \times 10^{23} \mathrm{atom}^{235} \mathrm{U}}{1 \mathrm{~mol}{ }^{235} \mathrm{U}} \times \frac{1 \mathrm{~J} \square \mathrm{s}^{2}}{1 \mathrm{~kg} \mathrm{~m}^{2}} \times \frac{1 \mathrm{~kJ}}{1 \times 10^{3} \mathrm{~J}}=$

Solution

Solution Steps

Step 1: Convert Atomic Mass Unit to Kilograms

The first step is to convert the atomic mass unit (amu) to kilograms using the conversion factor $1 \, \text{amu} = 1.6606 \times 10^{-27} \, \text{kg}$.

\[ \frac{0.19900718 \, \text{amu}}{1 \, \text{atom}^{235} \text{U}} \times \frac{1.6606 \times 10^{-27} \, \text{kg}}{1 \, \text{amu}} = 0.19900718 \times 1.6606 \times 10^{-27} \, \text{kg/atom}^{235} \text{U} \]

Step 2: Apply the Speed of Light Squared

Next, apply the speed of light squared, $(2.9979 \times 10^8 \, \text{m/s})^2$, to convert the mass to energy.

\[ 0.19900718 \times 1.6606 \times 10^{-27} \times (2.9979 \times 10^8)^2 \, \text{kg m}^2/\text{s}^2/\text{atom}^{235} \text{U} \]

Step 3: Convert Atoms to Moles

Convert the energy per atom to energy per mole using Avogadro's number, $6.022 \times 10^{23} \, \text{atoms/mol}$.

\[ 0.19900718 \times 1.6606 \times 10^{-27} \times (2.9979 \times 10^8)^2 \times 6.022 \times 10^{23} \, \text{kg m}^2/\text{s}^2/\text{mol}^{235} \text{U} \]

Step 4: Convert Joules to Kilojoules

Convert the energy from joules to kilojoules using the conversion factor $1 \, \text{kJ} = 10^3 \, \text{J}$.

\[ 0.19900718 \times 1.6606 \times 10^{-27} \times (2.9979 \times 10^8)^2 \times 6.022 \times 10^{23} \times \frac{1 \, \text{kJ}}{10^3 \, \text{J}} \, \text{kJ/mol}^{235} \text{U} \]