It is estimated that the energy released in the explosion of atomic bomb at Hiroshima was `9 xx 10^13`J. If an average 200MeV of energy is released in the fission of one , `._92U^235`. The mass of uranium used for the bomb is nearly

Options

A. 1.1 kg
B. 2.5 kg
C. 3.6 kg
D. 4 kg

Answer

To solve the problem step by step, we need to find the mass of uranium-235 used in the atomic bomb explosion based on the energy released.

### Step 1: Convert the total energy from Joules to Electron Volts
The total energy released in the explosion is given as \( 9 \times 10^{13} \) J. We know that:
\[ 1 \text{ eV} = 1.6 \times 10^{-19} \text{ J} \]
To convert Joules to Electron Volts, we use the conversion:
\[ \text{Energy in eV} = \frac{\text{Energy in J}}{1.6 \times 10^{-19}} \]
Substituting the given energy:
\[ \text{Energy in eV} = \frac{9 \times 10^{13}}{1.6 \times 10^{-19}} \approx 5.625 \times 10^{32} \text{ eV} \]

### Step 2: Calculate the number of fission events
Each fission of uranium-235 releases an average of 200 MeV of energy. First, we convert MeV to eV:
\[ 200 \text{ MeV} = 200 \times 10^6 \text{ eV} = 2 \times 10^8 \text{ eV} \]
Now, we can find the number of fission events (or uranium atoms that underwent fission) by dividing the total energy by the energy per fission:
\[ \text{Number of fissions} = \frac{\text{Total Energy in eV}}{\text{Energy per fission in eV}} = \frac{5.625 \times 10^{32}}{2 \times 10^8} \approx 2.8125 \times 10^{24} \]

### Step 3: Calculate the mass of uranium-235
To find the mass of uranium-235 used, we need to calculate the number of moles of uranium. The number of moles is given by:
\[ \text{Number of moles} = \frac{\text{Number of atoms}}{N_A} \]
where \( N_A \) (Avogadro's number) is approximately \( 6.022 \times 10^{23} \) atoms/mol. Thus:
\[ \text{Number of moles} = \frac{2.8125 \times 10^{24}}{6.022 \times 10^{23}} \approx 4.68 \text{ mol} \]
The molar mass of uranium-235 is approximately 235 g/mol. Therefore, the mass of uranium is:
\[ \text{Mass} = \text{Number of moles} \times \text{Molar mass} = 4.68 \text{ mol} \times 235 \text{ g/mol} \approx 1100 \text{ g} \]
Converting grams to kilograms:
\[ \text{Mass in kg} \approx 1.1 \text{ kg} \]

### Conclusion
Thus, the mass of uranium used for the bomb is nearly **1.1 kg**.