Answered

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What is the energy of a photon with a frequency of [tex]$1.7 \times 10^{17} \text{ Hz}$[/tex]? Planck's constant is [tex]$6.63 \times 10^{-34} \text{ J} \cdot \text{s}$[/tex].

A. [tex][tex]$1.1 \times 10^{-17} \text{ J}$[/tex][/tex]
B. [tex]$1.1 \times 10^{-16} \text{ J}$[/tex]
C. [tex]$8.3 \times 10^{-16} \text{ J}$[/tex]
D. [tex][tex]$8.3 \times 10^{-15} \text{ J}$[/tex][/tex]

Sagot :

GinnyAnsweridn
To determine the energy of a photon, 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]\((6.63 \times 10^{-34} J \cdot s)\)[/tex],
- [tex]\( f \)[/tex] is the frequency of the photon [tex]\((1.7 \times 10^{17} Hz)\)[/tex].

Substituting the given values into the formula:

[tex]\[ E = (6.63 \times 10^{-34} J\cdot s) \times (1.7 \times 10^{17} Hz) \][/tex]

Multiplying these values, we find:

[tex]\[ E = 1.1271 \times 10^{-16} J \][/tex]

Thus, the energy of the photon is [tex]\(1.1271 \times 10^{-16} J\)[/tex].

Among the given options:
- [tex]\(1.1 \times 10^{-17} J\)[/tex]
- [tex]\(1.1 \times 10^{-16} J\)[/tex]
- [tex]\(8.3 \times 10^{-16} J\)[/tex]
- [tex]\(8.3 \times 10^{-15} J\)[/tex]

The closest answer is [tex]\(1.1 \times 10^{-16} J\)[/tex].

Therefore, the correct option is:

[tex]\[ 1.1 \times 10^{-16} J \][/tex]
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