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What is the frequency of a photon with an energy of [tex]$3.38 \times 10^{-19} J$[/tex]?

A. [tex]$6.71 \times 10^{14} Hz$[/tex]

B. [tex][tex]$5.10 \times 10^{14} Hz$[/tex][/tex]

C. [tex]$1.96 \times 10^{14} Hz$[/tex]

D. [tex]$4.47 \times 10^{14} Hz$[/tex]


Sagot :

To find the frequency of a photon given its energy, we can 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, and
- [tex]\( f \)[/tex] is the frequency.

Given values:
- Energy [tex]\( E = 3.38 \times 10^{-19} \)[/tex] Joules
- Planck's constant [tex]\( h = 6.626 \times 10^{-34} \)[/tex] Joule seconds

We can rearrange the formula to solve for frequency [tex]\( f \)[/tex]:

[tex]\[ f = \frac{E}{h} \][/tex]

Substitute the given values into the formula:

[tex]\[ f = \frac{3.38 \times 10^{-19}}{6.626 \times 10^{-34}} \][/tex]

Carrying out the division, we obtain:

[tex]\[ f = 5.10 \times 10^{14} \text{ Hz} \][/tex]

Therefore, the frequency of the photon is [tex]\( 5.10 \times 10^{14} \)[/tex] Hz, which corresponds to option B.