If in nuclear fission, a piece of uranium of mass 6.0 g is lost, the energy obtained (in kWh) is `n xx 10^(7)`. Find the value of n.

Answer

To find the value of \( n \) in the energy obtained from the nuclear fission of a piece of uranium with a mass loss of 6.0 g, we can follow these steps:

### Step 1: Convert mass from grams to kilograms
Given that the mass lost is 6.0 g, we convert this to kilograms:
\[ \Delta m = 6.0 \, \text{g} = 6.0 \times 10^{-3} \, \text{kg} \]

**Hint:** Remember that 1 g = \( 10^{-3} \) kg.

### Step 2: Use Einstein's equation to calculate energy
According to Einstein's mass-energy equivalence principle, the energy \( E \) corresponding to the mass lost can be calculated using the formula:
\[ E = \Delta m c^2 \]
where \( c \) (the speed of light) is approximately \( 3 \times 10^8 \, \text{m/s} \).

Substituting the values:
\[ E = (6.0 \times 10^{-3} \, \text{kg}) \times (3 \times 10^8 \, \text{m/s})^2 \]

### Step 3: Calculate \( c^2 \)
Calculating \( c^2 \):
\[ c^2 = (3 \times 10^8)^2 = 9 \times 10^{16} \, \text{m}^2/\text{s}^2 \]

### Step 4: Substitute \( c^2 \) back into the energy equation
Now substituting \( c^2 \) back into the energy equation:
\[ E = 6.0 \times 10^{-3} \times 9 \times 10^{16} \]

### Step 5: Perform the multiplication
Calculating the energy:
\[ E = 54 \times 10^{13} \, \text{J} \]

### Step 6: Convert energy from joules to kilowatt-hours
To convert joules to kilowatt-hours, use the conversion factor \( 1 \, \text{kWh} = 3.6 \times 10^6 \, \text{J} \):
\[ E_{\text{kWh}} = \frac{54 \times 10^{13} \, \text{J}}{3.6 \times 10^6 \, \text{J/kWh}} \]

### Step 7: Calculate the value
Calculating the division:
\[ E_{\text{kWh}} = \frac{54}{3.6} \times 10^{13 - 6} = 15 \times 10^{7} \, \text{kWh} \]

### Step 8: Identify the value of \( n \)
From the expression \( E_{\text{kWh}} = n \times 10^7 \), we see that:
\[ n = 15 \]

### Final Answer
Thus, the value of \( n \) is:
\[ \boxed{15} \]

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