To find the total energy generated by the Sun in a year, we need to multiply the energy generated per second by the total number of seconds in a year.
Given:
- Energy generated by the Sun per second: \(4 \times 10^{26}\) joules
- Number of seconds in a year: \(3.15 \times 10^{7}\) seconds
The total energy generated in a year is calculated as follows:
\[
\text{Total energy} = \text{Energy per second} \times \text{Number of seconds in a year}
\]
Substituting in the values:
\[
\text{Total energy} = (4 \times 10^{26} \text{ joules/second}) \times (3.15 \times 10^{7} \text{ seconds})
\]
Now, multiply the coefficients and add the exponents:
\[
\text{Total energy} = 4 \times 3.15 \times 10^{26} \times 10^{7}
\]
Calculating \(4 \times 3.15\):
\[
4 \times 3.15 = 12.6
\]
Then combine the powers of ten:
\[
\text{Total energy} = 12.6 \times 10^{26 + 7} = 12.6 \times 10^{33}
\]
To express \(12.6\) in scientific notation, we can write it as \(1.26 \times 10^{1}\):
\[
\text{Total energy} = 1.26 \times 10^{1} \times 10^{33} = 1.26 \times 10^{34}
\]
Thus, the total energy generated by the Sun in one year is:
\[
\boxed{1.26 \times 10^{34}} \text{ joules}
\]
