The distance of a galaxy from the earth is of the order of `10^(25)m`. The time taken by light to reach the earth from the galaxy is

Options

A. `A. 3xx10^(14)s`
B. `B. 3xx10^(16)s`
C. C. `3xx10^(18)s`
D. `D. 3xx10^(20)s`

Explanation

To solve the problem of finding the time taken by light to reach Earth from a galaxy that is \(10^{25}\) meters away, we will follow these steps:

### Step 1: Write down the given values
We know:
- Distance \(d = 10^{25}\) meters
- Speed of light \(c = 3 \times 10^{8}\) meters per second

### Step 2: Use the formula for time
The time \(t\) taken for light to travel a distance can be calculated using the formula:
\[ t = \frac{d}{c} \]

### Step 3: Substitute the values into the formula
Now, substituting the known values into the formula:
\[ t = \frac{10^{25}}{3 \times 10^{8}} \]

### Step 4: Simplify the expression
We can simplify the expression by separating the powers of ten:
\[ t = \frac{10^{25}}{10^{8}} \times \frac{1}{3} = 10^{(25-8)} \times \frac{1}{3} = 10^{17} \times \frac{1}{3} \]

### Step 5: Calculate the numerical value
Calculating \(\frac{1}{3}\) gives approximately \(0.33\), so:
\[ t \approx 0.33 \times 10^{17} \text{ seconds} \]

### Step 6: Express in scientific notation
We can express \(0.33\) as \(3.33\) and adjust the power of ten:
\[ t \approx 3.33 \times 10^{16} \text{ seconds} \]

### Step 7: Round to match the options
Since the options provided are in the form of \(3 \times 10^{16}\), we can round \(3.33\) to \(3\):
\[ t \approx 3 \times 10^{16} \text{ seconds} \]

### Conclusion
Thus, the time taken by light to reach Earth from the galaxy is approximately:
\[ \text{Option B: } 3 \times 10^{16} \text{ seconds} \]

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