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A photon has a frequency of [tex]2.9 \times 10^{-16} \, \text{Hz}[/tex]. Planck's constant is [tex]6.63 \times 10^{-34} \, \text{J} \cdot \text{s}[/tex].

The energy of the photon, to the nearest tenths place, is [tex]\square \times 10^{-49} \, \text{J}[/tex].

Sagot :

GinnyAnsweridn
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]
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