Calculate the energy of a photon of light with a frequency of [tex]4.35 \times 10^{14} \, \text{Hz}[/tex]. (Planck's constant: [tex]h = 6.63 \times 10^{-34} \, \text{J} \cdot \text{s}[/tex])

A. [tex]2.88 \times 10^{-19} \, \text{J}[/tex]
B. [tex]3.25 \times 10^{-19} \, \text{J}[/tex]
C. [tex]4.56 \times 10^{-19} \, \text{J}[/tex]
D. [tex]5.28 \times 10^{-19} \, \text{J}[/tex]



Answer :

To calculate the energy of a photon given its frequency, we can use Planck's equation:

[tex]\[ E = h \nu \][/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]\( \nu \)[/tex] (the Greek letter "nu") is the frequency of the photon.

Given data:
- The frequency ([tex]\( \nu \)[/tex]) is [tex]\( 4.35 \times 10^{14} \, \text{Hz} \)[/tex].

Substitute the values into the equation:

[tex]\[ E = (6.63 \times 10^{-34} \, \text{J} \cdot \text{s}) \times (4.35 \times 10^{14} \, \text{Hz}) \][/tex]

Performing the multiplication:

1. Multiply the numeric parts:
[tex]\[ 6.63 \times 4.35 = 28.8845 \][/tex]

2. Combine the powers of 10:
[tex]\[ 10^{-34} \times 10^{14} = 10^{-20} \][/tex]

So combining both steps:

[tex]\[ E = 28.8845 \times 10^{-20} \][/tex]

Convert this to scientific notation:
[tex]\[ 28.8845 \times 10^{-20} = 2.88845 \times 10^{-19} \][/tex]

Given the solution options and focusing on significant figures, we round the energy to three significant figures:

[tex]\[ E \approx 2.88 \times 10^{-19} \, \text{J} \][/tex]

Therefore, the energy of the photon is:

[tex]\[ \boxed{2.88 \times 10^{-19} \, \text{J}} \][/tex]

This matches the first option provided.