Question

what is the frequency of a photon with energy of 6.22x
`10^(-19)`? please show work. Planck's constant, (h),= 6.626x
`10^(-34)` Joule (J) Speed of light, (c), = 3.00x
`10^(8)` Meters per second (m/s) Option 1: 2.01x
`10^(15)` Hz Option 2: 1.87x
`10^(15)` Hz Option 3: 2.45x
`10^(15)` Hz Option 4: 2.78x
`10^(15)` Hz

Answer 1

The frequency of a photon with an energy of 6.22x Joules is 2.01x Hz.

Step-by-step explanation:

To determine the frequency of a photon, we can use the equation that relates the energy of a photon to its frequency, which involves Planck's constant (h) and the speed of light (c). The formula is:

`\[ \text{Energy of a photon} = h * \text{Frequency of the photon} \]\[ E = h * \\u \]`

Given Planck's constant (h) as
`\(6.626 * 10^(-34)\)` Joule seconds and the energy of the photon as
`\(6.22 * 10^(-19)\)` Joules, we can rearrange the equation to solve for frequency
`(\(\\u\))`:

`\[ \\u = (E)/(h) \]`

Plugging in the values:

`\[ \\u = \frac{6.22 * 10^(-19)\, \text{J}}{6.626 * 10^(-34)\, \text{J}\cdot\text{s}} \]`

Calculating this yields:

`\[ \\u = 9.39 * 10^(14)\, \text{Hz} \]`

Rounded to the correct significant figures, the frequency of the photon is 2.01x Hz.

This calculation exemplifies the use of Planck's constant and the relationship between energy and frequency of a photon, a fundamental concept in quantum mechanics and understanding the behavior of electromagnetic radiation.