If the speed of light were `2//3` of its present value, the energy released in a given atomic explosion will be decreased by a fraction.

Options

A. `2//3`
B. `4//9`
C. `3//4`
D. `5//9`

Explanation

To solve the problem, we need to analyze how the energy released in an atomic explosion changes when the speed of light is altered. The energy released in such an explosion is given by the equation:

\[ E = mc^2 \]

where:
- \( E \) is the energy,
- \( m \) is the mass,
- \( c \) is the speed of light.

### Step 1: Understand the relationship between energy and the speed of light
The energy released is directly proportional to the square of the speed of light. This means if the speed of light changes, the energy will change according to the square of that change.

### Step 2: Define the new speed of light
According to the problem, the new speed of light \( c' \) is given as:

\[ c' = \frac{2}{3}c \]

### Step 3: Calculate the new energy
Using the new speed of light, we can calculate the new energy \( E' \):

\[ E' = m(c')^2 \]
\[ E' = m\left(\frac{2}{3}c\right)^2 \]
\[ E' = m\left(\frac{4}{9}c^2\right) \]
\[ E' = \frac{4}{9}mc^2 \]

### Step 4: Relate the new energy to the original energy
Now, we can relate the new energy \( E' \) to the original energy \( E \):

\[ E = mc^2 \]
Thus, we can express \( E' \) in terms of \( E \):

\[ E' = \frac{4}{9}E \]

### Step 5: Determine the fraction decrease in energy
To find the fraction by which the energy has decreased, we can calculate:

1. The original energy \( E \) is 1 (or \( \frac{9}{9}E \)).
2. The new energy \( E' \) is \( \frac{4}{9}E \).

The decrease in energy is:

\[ \text{Decrease} = E - E' = E - \frac{4}{9}E = \frac{5}{9}E \]

### Step 6: Calculate the fraction of decrease
The fraction of decrease in energy is given by:

\[ \text{Fraction Decrease} = \frac{\text{Decrease}}{E} = \frac{\frac{5}{9}E}{E} = \frac{5}{9} \]

Thus, the energy released in a given atomic explosion will be decreased by a fraction of \( \frac{5}{9} \).

### Final Answer
The energy released in a given atomic explosion will be decreased by a fraction of \( \frac{5}{9} \).

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