Chapter 19.14, Problem 1QP

To determine

To demonstrate:

The frequency and energy of a photon of visible light.

Answer to Problem 1QP

The frequency and energy of a photon of visible light is $\underset{\_}{6\times {10}^{14}{\text{s}}^{-1}}$ and $\underset{\_}{3.98\times {10}^{-19}\text{J}}$ respectively.

Explanation of Solution

Given:

The wavelength of a visible light, $\lambda =5\times {10}^{-7}\text{m}$.

Explanation:

Write the equation of frequency of a photon of green light.

$\nu =\frac{c}{\lambda }$ (I)

Here, the velocity of light is c.

Determine the energy of a photon of visible light.

$E=\frac{hc}{\lambda }$ (II)

Here, the universal constant is h.

Conclusion:

Substitute $3\times {10}^8\text{m/s}$ for c and $5\times {10}^{-7}\text{m}$ for $\lambda$ in Equation (I).

$\begin{array}{c}\nu =\frac{3\times {10}^8\text{m/s}}{5\times {10}^{-7}\text{m}}\\ =6\times {10}^{14}{\text{s}}^{-1}\end{array}$

Substitute $3\times {10}^8\text{m/s}$ for c, $5\times {10}^{-7}\text{m}$ for $\lambda$, and $6.63\times {10}^{-34}\text{J}\cdot \text{s}$ for h in Equation (II).

$\begin{array}{c}E=\frac{\left(6.63\times {10}^{-34}\text{J}\cdot \text{s}\right)\left(3\times {10}^8\text{m/s}\right)}{5\times {10}^{-7}\text{m}}\\ =3.98\times {10}^{-19}\text{J}\end{array}$

Thus, the frequency and energy of a photon of visible light is $\underset{\_}{6\times {10}^{14}{\text{s}}^{-1}}$ and $\underset{\_}{3.98\times {10}^{-19}\text{J}}$ respectively.