What is the energy of light with a frequency of $$ 3 \times 10^{9} \mathrm{~Hz} $$ ? $$ \mathrm{h}=6.626 \times 10^{-34} \mathrm{~J} \cdot \mathrm{~s} $$ $$ [?] \times 10^{[?]} \mathrm{J} $$

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UpStudy AI · Accepted Answer

To calculate the energy $$ E $$ of light with a frequency $$ \nu $$, you can use the equation:

$$
E = h \nu
$$

Where:
- $$ h $$ is Planck's constant $$ (6.626 \times 10^{-34} \, \mathrm{J} \cdot \mathrm{s}) $$
- $$ \nu $$ is the frequency of the light

Given:
$$
\nu = 3 \times 10^{9} \, \mathrm{Hz}
$$

Plugging in the values:

$$
E = 6.626 \times 10^{-34} \, \mathrm{J} \cdot \mathrm{s} \times 3 \times 10^{9} \, \mathrm{Hz}
$$

$$
E = (6.626 \times 3) \times 10^{-34 + 9} \, \mathrm{J}
$$

$$
E = 19.878 \times 10^{-25} \, \mathrm{J}
$$

Rounding to two significant figures:

$$
E \approx 1.98 \times 10^{-24} \, \mathrm{J}
$$

**Final Answer:**
$$
E = 1.99 \times 10^{-24} \, \mathrm{J}
$$
The energy of the light is $$ 1.99 \times 10^{-24} \, \mathrm{J} $$.

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a frequency of ?

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