To find the energy of a photon given its frequency, we use the formula:
[tex]\[ E = h \cdot f \][/tex]
Where:
- [tex]\( E \)[/tex] is the energy of the photon,
- [tex]\( h \)[/tex] is Planck's constant ([tex]\( 6.63 \times 10^{-34} \, \text{J} \cdot \text{s} \)[/tex]),
- [tex]\( f \)[/tex] is the frequency of the photon ([tex]\( 2.9 \times 10^{-16} \, \text{Hz} \)[/tex]).
First, let's calculate the energy [tex]\( E \)[/tex]:
[tex]\[ E = 6.63 \times 10^{-34} \, \text{J} \cdot \text{s} \times 2.9 \times 10^{-16} \, \text{Hz} \][/tex]
Performing the multiplication:
[tex]\[ E = (6.63 \times 2.9) \times (10^{-34} \times 10^{-16}) \, \text{J} \][/tex]
[tex]\[ E = 19.227 \times 10^{-50} \, \text{J} \][/tex]
Rewriting this in the standard scientific notation:
[tex]\[ E = 1.9227 \times 10^{-49} \, \text{J} \][/tex]
Now, we need to convert the energy to the nearest tenths place in the form:
[tex]\[ a \times 10^{-49} \, \text{J} \][/tex]
Here, [tex]\( a \)[/tex] is the coefficient rounded to the nearest tenths place. Given [tex]\( 1.9227 \)[/tex], rounding to the nearest tenth, we get:
[tex]\[ a = 1.9 \][/tex]
So, the energy of the photon, to the nearest tenths place, is:
[tex]\[ 1.9 \times 10^{-49} \, \text{J} \][/tex]
