Question

1. what is the energy of a 7.66×10¹⁴ hz wave?
2. what is the frequency of a wave carrying 8.35×10⁻¹⁹ j of energy?
3. what is the frequency of a 1.78×10¹⁵ j wave?
4. what is the energy of a 3.12×10¹⁴ s⁻¹ wave?
5. what is the frequency of a 1.31×10²² j wave?
6. what is the wavelength of a 7.65×10⁻¹⁷ j wave? what is its wavelength?
7. what is the energy of a 9,330 cm wave?
8. what is the wavelength of a 1.528×10⁻¹³ j wave?

Explanation:

11.

Step1: Recall energy - frequency formula

The energy of a photon is given by $E = h
u$, where $E$ is energy, $h = 6.63\times10^{- 34}\text{ J}\cdot\text{s}$ (Planck's constant) and $
u$ is frequency. First, we need to convert the wavelength $\lambda = 4.257\times10^{7}\text{ cm}$ to meters. Since $1\text{ m}=100\text{ cm}$, $\lambda=4.257\times10^{5}\text{ m}$. Then use the wave - speed formula $c = \lambda
u$ ($c = 3\times10^{8}\text{ m/s}$), so $
u=\frac{c}{\lambda}$.
$
u=\frac{3\times10^{8}\text{ m/s}}{4.257\times10^{5}\text{ m}}\approx704.7\text{ Hz}$
Then $E = h
u=6.63\times10^{-34}\text{ J}\cdot\text{s}\times704.7\text{ Hz}\approx4.67\times10^{-31}\text{ J}$

12.

Step1: Use energy - frequency formula

Given $
u = 7.66\times10^{14}\text{ Hz}$, and $E = h
u$ with $h = 6.63\times10^{-34}\text{ J}\cdot\text{s}$.
$E=6.63\times10^{-34}\text{ J}\cdot\text{s}\times7.66\times10^{14}\text{ Hz}\approx5.08\times10^{-19}\text{ J}$

13.

Step1: Rearrange energy - frequency formula

Given $E = 8.35\times10^{-19}\text{ J}$ and $E = h
u$. We can solve for $
u$ by $
u=\frac{E}{h}$.
$
u=\frac{8.35\times10^{-19}\text{ J}}{6.63\times10^{-34}\text{ J}\cdot\text{s}}\approx1.26\times10^{15}\text{ Hz}$

14.

Answer:

1. Energy $\approx4.67\times10^{-31}\text{ J}$
2. Energy $\approx5.08\times10^{-19}\text{ J}$
3. Frequency $\approx1.26\times10^{15}\text{ Hz}$
4. Energy $\approx1.18\times10^{-18}\text{ J}$
5. Energy $\approx2.07\times10^{-19}\text{ J}$
6. Frequency $\approx1.98\times10^{11}\text{ Hz}$, Wavelength $\approx1.52\text{ mm}$
7. Energy for first part $\approx1.15\times10^{17}\text{ Hz}$ - related energy, Energy for second part $\approx2.14\times10^{-27}\text{ J}$
8. Wavelength $\approx1.30\times10^{-12}\text{ m}$