A nucleus kept at rest in free space, brakes up into smaller nuclei of masses `'m'` and `'2m'`. Total energy generated in this fission is `E`. The bigger part is radioactive, emits five gamma ray photons in the direction opposite to its velocity and finally comes torest. `["Given" h=6.6xx10^(-34)Js,m=1xx10^(-26)Kg,E= 3.63xx10^(-8) mc^(2), C=3xx10^(8)m//s)`
Fractional loss of mass in the fission is

Options

A. `1.21 xx10^(-8)`
B. `2.56xx10^(-8)`
C. 1.73xx10^(-8)`
D. `3.52 xx 10^(-8)`

Explanation

To solve the problem of fractional loss of mass during the fission of a nucleus, we can follow these steps:

### Step 1: Understanding the Problem
We have a nucleus that breaks into two smaller nuclei of masses `m` and `2m`. The total energy generated in this fission is given as `E`. The larger nucleus emits five gamma ray photons and comes to rest. We need to find the fractional loss of mass during this fission process.

### Step 2: Relate Energy to Mass Loss
According to the mass-energy equivalence principle, the change in mass (Δm) can be related to the energy (E) generated during the fission using the equation:
\[ \Delta m c^2 = E \]
From this, we can express the change in mass as:
\[ \Delta m = \frac{E}{c^2} \]

### Step 3: Substitute the Given Energy
We are given that:
\[ E = 3.63 \times 10^{-8} m c^2 \]
Substituting this into our equation for Δm gives:
\[ \Delta m = \frac{3.63 \times 10^{-8} m c^2}{c^2} \]
The \( c^2 \) terms cancel out:
\[ \Delta m = 3.63 \times 10^{-8} m \]

### Step 4: Calculate the Total Mass After Fission
The total mass before fission is the mass of the original nucleus, which is \( 3m \) (since it breaks into masses \( m \) and \( 2m \)). After the fission, the total mass is:
\[ \text{Total mass after fission} = m + 2m - \Delta m = 3m - \Delta m \]

### Step 5: Calculate Fractional Loss of Mass
The fractional loss of mass (F) can be calculated using the formula:
\[ F = \frac{\Delta m}{\text{Initial mass}} \]
Substituting the values we have:
\[ F = \frac{\Delta m}{3m} = \frac{3.63 \times 10^{-8} m}{3m} \]
The \( m \) terms cancel out:
\[ F = \frac{3.63 \times 10^{-8}}{3} \]
Calculating this gives:
\[ F = 1.21 \times 10^{-8} \]

### Final Answer
The fractional loss of mass in the fission is:
\[ F = 1.21 \times 10^{-8} \]

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