Question

instructions: answer the questions below regarding light a and light b: light a frequency: 4.15 x 10^13 hz light b frequency: 7.40 x 10^13 hz 4) calculate the wavelengths of light a and light b: 5) which of the lights (a or b) is more likely to be a violet light? why? 6) which of the lights (a or b) is more likely to be a red light? why? 7) which of the lights will release waves with a lower energy? how do you know? 8) to create an orange light, how would you change the wavelength of light a?

Explanation:

Step1: Recall the formula for wavelength

The speed - of - light formula is $c = \lambda
u$, where $c = 3\times10^{8}\ m/s$ (speed of light in a vacuum), $\lambda$ is the wavelength, and $
u$ is the frequency. So, $\lambda=\frac{c}{
u}$.

Step2: Calculate the wavelength of Light A

For Light A with $
u_A = 4.15\times 10^{13}\ Hz$, $\lambda_A=\frac{3\times 10^{8}\ m/s}{4.15\times 10^{13}\ Hz}\approx7.23\times 10^{-6}\ m$.

Step3: Calculate the wavelength of Light B

For Light B with $
u_B = 7.40\times 10^{13}\ Hz$, $\lambda_B=\frac{3\times 10^{8}\ m/s}{7.40\times 10^{13}\ Hz}\approx4.05\times 10^{-6}\ m$.

Step4: Answer question 5

Violet light has a shorter wavelength and higher frequency in the visible - light spectrum. Since $
u_B>
u_A$ and $\lambda_B < \lambda_A$, Light B is more likely to be violet light.

Step5: Answer question 6

Red light has a longer wavelength and lower frequency in the visible - light spectrum. Since $
u_A<
u_B$ and $\lambda_A>\lambda_B$, Light A is more likely to be red light.

Step6: Answer question 7

The energy of a photon is given by $E = h
u$, where $h$ is Planck's constant ($h = 6.63\times 10^{-34}\ J\cdot s$). Since $E\propto
u$, and $
u_A<
u_B$, Light A will release waves with lower energy.

Step7: Answer question 8

Orange light has a shorter wavelength than red light but longer than yellow light. Since Light A is more likely to be red - like (from question 6), to create an orange light, we need to decrease the wavelength of Light A.

Answer:

1. $\lambda_A\approx7.23\times 10^{-6}\ m$, $\lambda_B\approx4.05\times 10^{-6}\ m$
2. Light B, because it has a higher frequency and shorter wavelength like violet light.
3. Light A, because it has a lower frequency and longer wavelength like red light.
4. Light A, because energy $E = h

u$ and it has a lower frequency.

1. Decrease the wavelength of Light A.