Question

1. a wave has a frequency of 3.0 × 10¹⁴ hz. calculate the wavelength.
2. what is the energy of a photon with a frequency of 6.0 × 10¹⁴ hz?
3. which color of visible light has the highest energy? (a) red (b) green (c) blue (d) violet

Explanation:

Step1: Recall the formula for energy of a photon

The energy of a photon is given by \(E = h
u\), where \(h = 6.63\times10^{-34}\space Js\) (Planck's constant) and \(
u\) is the frequency.

Step2: Substitute the given values

Given \(
u=6.0\times 10^{14}\space Hz\), we substitute into the formula:
\(E=(6.63\times 10^{-34}\space Js)\times(6.0\times 10^{14}\space Hz)\)

Step3: Calculate the energy

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for wavelength calculation:

Step1: Recall the formula for the speed of light

The speed of light \(c=\lambda
u\), where \(c = 3\times10^{8}\space m/s\), \(\lambda\) is the wavelength and \(
u\) is the frequency.

Step2: Solve for wavelength

\(\lambda=\frac{c}{
u}\)

Step3: Substitute the given values

Given \(
u = 3.0\times10^{14}\space Hz\) and \(c = 3\times10^{8}\space m/s\)
\(\lambda=\frac{3\times 10^{8}\space m/s}{3.0\times 10^{14}\space Hz}\)

Step4: Calculate the wavelength

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The energy of a photon is directly proportional to its frequency (\(E = h
u\)). In the visible light spectrum, violet light has the highest frequency among the given options (red, green, blue, violet). Since energy is proportional to frequency, violet light has the highest energy.

Answer:

1. The energy of the photon is \(3.978\times 10^{-19}\space J\)
2. The wavelength of the wave is \(1\times 10^{-6}\space m\)

For question 13: