Question

calculate the energy & identify the type of electromagnetic radiation with a wavelength of 4.9x10^-4m

Answer 1

The energy of the electromagnetic radiation with a wavelength of
`\(4.9 * 10^(-4) \, \text{m}\)` is approximately
`\(4.05 * 10^(-19) \, \text{J}\).` This wavelength corresponds to the infrared region of the spectrum.

To calculate the energy
`(\(E\))` of electromagnetic radiation, you can use the following formula:

`\[ E = h \cdot \\u \]`

where:

-
`\(E\)` is the energy,

-
`\(h\)` is Planck's constant
`(\(6.626 * 10^(-34) \, \text{J} \cdot \text{s}\))`,

-
`\(\\u\)` is the frequency.

The frequency
`(\(\\u\))` is related to the wavelength
`(\(\lambda\))` by the speed of light
`(\(c\))`:

`\[ \\u = (c)/(\lambda) \]`

where:

-
`\(\\u\)` is the frequency,

-
`\(c\)` is the speed of light
`(\(3.00 * 10^8 \, \text{m/s}\))`,

-
`\(\lambda\)` is the wavelength.

Given that the wavelength
`(\(\lambda\))` is
`\(4.9 * 10^(-4) \, \text{m}\)`, we can first find the frequency
`(\(\\u\))` using the second formula, and then use it to find the energy
`(\(E\))`.

1. Calculate Frequency
`(\(\\u\))`:

`\[ \\u = (c)/(\lambda) \]`

`\[ \\u = \frac{3.00 * 10^8 \, \text{m/s}}{4.9 * 10^(-4) \, \text{m}} \]`

2. Calculate Energy
`(\(E\))`:

`\[ E = h \cdot \\u \]`

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

Perform the calculations to find the values of
`\(\\u\)` and
`\(E\)`.

`\[ \\u \approx 6.12 * 10^(14) \, \text{Hz} \]`

`\[ E \approx (6.626 * 10^(-34) \, \text{J} \cdot \text{s}) * (6.12 * 10^(14) \, \text{Hz}) \]`

`\[ E \approx 4.05 * 10^(-19) \, \text{J} \]`

So, the energy of the electromagnetic radiation with a wavelength of
`\(4.9 * 10^(-4) \, \text{m}\)` is approximately
`\(4.05 * 10^(-19) \, \text{J}\).`

To identify the type of electromagnetic radiation, we can use the electromagnetic spectrum. In general terms, this wavelength corresponds to the infrared region of the spectrum.