To calculate the energy of a photon, you can use the formula:
\[ E = h \cdot f \]
where:
- \( E \) is the energy of the photon,
- \( h \) is Planck's constant (\( 6.63 \times 10^{-34} , \text{J}\cdot\text{s} \)),
- \( f \) is the frequency of the photon (\( 2.9 \times 10^{-16} , \text{Hz} \)).
Now, let's plug in the values:
\[ E = (6.63 \times 10^{-34} , \text{J}\cdot\text{s}) \cdot (2.9 \times 10^{-16} , \text{Hz}) \]
Now, calculate \( E \):
\[ E = 6.63 \times 2.9 \times 10^{-34} \times 10^{-16} \]
Calculating \( 6.63 \times 2.9 \):
\[ 6.63 \times 2.9 = 19.227 \]
Now, multiply the powers of 10:
\[ 10^{-34} \times 10^{-16} = 10^{-50} \]
Now, assemble it all together:
\[ E = 19.227 \times 10^{-50} , \text{J} \]
To express this in scientific notation:
\[ E = 1.9227 \times 10^{-49} , \text{J} \]
Now, rounding to the nearest tenths place:
\[ E \approx 1.9 \times 10^{-49} , \text{J} \]
Thus, the energy of the photon, to the nearest tenths place, is:
\[ \boxed{1.9 \times 10^{-49}} , \text{J} \]
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