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Calculate the energy of a photon of light with a frequency of [tex]6.95 \times 10^{14} \, \text{Hz}[/tex].

(Planck's constant: [tex]h = 6.63 \times 10^{-34} \, \text{J} \cdot \text{s}[/tex])

A. [tex]1.04 \times 10^{-5} \, \text{J}[/tex]
B. [tex]2.87 \times 10^{-13} \, \text{J}[/tex]
C. [tex]4.61 \times 10^{-19} \, \text{J}[/tex]
D. [tex]5.67 \times 10^{-29} \, \text{J}[/tex]



Answer :

GinnyAnswer
To calculate the energy of a photon, we use the formula derived from Planck's relation, which states:

[tex]\[ E = h \cdot f \][/tex]

where:
- [tex]\( E \)[/tex] is the energy of the photon,
- [tex]\( h \)[/tex] is Planck's constant,
- [tex]\( f \)[/tex] is the frequency of the photon.

Given the values:
- Frequency [tex]\( f = 6.95 \times 10^{14} \text{ Hz} \)[/tex]
- Planck's constant [tex]\( h = 6.63 \times 10^{-34} \text{ J} \cdot \text{s} \)[/tex]

We substitute these values into the formula:

[tex]\[ E = (6.63 \times 10^{-34} \text{ J} \cdot \text{s}) \times (6.95 \times 10^{14} \text{ Hz}) \][/tex]

After performing the multiplication, we obtain:

[tex]\[ E = 4.61 \times 10^{-19} \text{ J} \][/tex]

Thus, the energy of a photon of light with a frequency of [tex]\( 6.95 \times 10^{14} \text{ Hz} \)[/tex] is:

[tex]\[ \boxed{4.61 \times 10^{-19} \text{ J}} \][/tex]