Question

if photons traveled directly form the core to the photosphere at the speed of light, how long would it take? the process of absorption, emission, and convection causes it to be much slower. how long does it actually take?

Explanation:

Step1: Know the distance and speed formula

The formula for time $t$ is $t=\frac{d}{v}$, where $d$ is distance and $v$ is speed. The distance from the Sun's core to the photosphere is approximately $d = 6.96\times 10^{8}\text{ m}$ and the speed of light $v=3\times 10^{8}\text{ m/s}$.

Step2: Calculate the direct - travel time

$t=\frac{6.96\times 10^{8}}{3\times 10^{8}} = 2.32\text{ s}$
The actual time due to absorption, emission and convection in the Sun's interior is about 100,000 - 1,000,000 years.

Answer:

Direct - travel time: 2.32 s; Actual time: 100,000 - 1,000,000 years