The energy released during the fussion of 1 kg uranium is

Options

A. `9 xx 10^(23) "ergs"`
B. `9.0 xx 10^(10) "ergs"`
C. `9.0 xx 10^(18) "ergs"`
D. `9.0 xx 10^(8) "ergs"`

Explanation

To find the energy released during the fission of 1 kg of uranium-235, we can follow these steps:

### Step 1: Calculate the number of moles of uranium-235
The formula to calculate the number of moles is:
\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molecular mass}} \]
Given mass = 1 kg = 1000 grams
Molecular mass of uranium-235 = 235 g/mol

\[ \text{Number of moles} = \frac{1000 \text{ g}}{235 \text{ g/mol}} \approx 4.2553 \text{ moles} \]

### Step 2: Calculate the energy released per atom
The average energy released during the fission of one uranium-235 atom is given as 215 MeV. To convert this to joules, we use the conversion factor:
\[ 1 \text{ MeV} = 1.6 \times 10^{-13} \text{ joules} \]
Thus,
\[ \text{Energy per atom} = 215 \text{ MeV} \times 1.6 \times 10^{-13} \text{ J/MeV} = 344 \times 10^{-13} \text{ J} \]

### Step 3: Calculate the total number of atoms in the moles of uranium
Using Avogadro's number, which is approximately \(6.022 \times 10^{23} \text{ atoms/mol}\):
\[ \text{Total number of atoms} = \text{Number of moles} \times \text{Avogadro's number} \]
\[ \text{Total number of atoms} = 4.2553 \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mol} \approx 2.558 \times 10^{24} \text{ atoms} \]

### Step 4: Calculate the total energy released
Now, we can find the total energy released by multiplying the energy released per atom by the total number of atoms:
\[ \text{Total energy released} = \text{Total number of atoms} \times \text{Energy per atom} \]
\[ \text{Total energy released} = 2.558 \times 10^{24} \text{ atoms} \times 344 \times 10^{-13} \text{ J/atom} \]
\[ \text{Total energy released} \approx 8.81 \times 10^{13} \text{ J} \]

### Step 5: Convert the total energy to a more convenient unit (if necessary)
To express this in terms of hertz, we can convert joules to hertz using the relation \(1 \text{ J} = 1 \text{ Hz}\) (in terms of energy per photon). However, it is more common to express energy in joules rather than hertz in this context.

Thus, the total energy released during the fission of 1 kg of uranium-235 is approximately:
\[ \text{Total energy} \approx 8.81 \times 10^{13} \text{ J} \]