To calculate the energy of one photon of light, we can use the formula:
\[ E = h \cdot f \]
where:
- \( E \) is the energy of the photon (in joules),
- \( h \) is Planck's constant (\(6.626 \times 10^{-34}\) J·s),
- \( f \) is the frequency of the light (in hertz).
Combining these values, we have:
Given:
- \( f = 7.06 \times 10^{14} , \text{Hz} \)
- \( h = 6.626 \times 10^{-34} , \text{Js} \)
Now we can calculate \( E \):
\[ E = (6.626 \times 10^{-34} , \text{Js}) \cdot (7.06 \times 10^{14} , \text{Hz}) \]
Calculating \( E \):
\[ E = 6.626 \times 7.06 \times 10^{-34} \times 10^{14} \]
Calculating \( 6.626 \times 7.06 \):
\[ 6.626 \times 7.06 = 46.88456 \]
So:
\[ E = 46.88456 \times 10^{-20} , \text{J} \]
Now converting this to significant figures (3 significant figures from the frequency), we have:
\[ E \approx 4.69 \times 10^{-19} , \text{J} \]
Thus, the energy of exactly one photon of this light is approximately:
\[ \boxed{4.69 \times 10^{-19} , \text{J}} \]