Question

1. a green laser pointer emits light at a wavelength of 532 nm. what is the energy of a single photon of this light? a. 3.74 × 10⁻¹⁹ j b. 5.55 × 10¹² j c. 4.34 × 10⁻¹¹ j d. 3.34 × 10⁻¹⁵ j e. 4.36 × 10⁻¹⁸ j

Explanation:

Step1: Recall photon energy formula

The energy of a photon is given by \( E = h
u \), and since \( c=\lambda
u \) (where \( c \) is the speed of light, \( \lambda \) is wavelength, \(
u \) is frequency), we can substitute \(
u=\frac{c}{\lambda} \) into the energy formula to get \( E = \frac{hc}{\lambda} \). Here, \( h = 6.626\times 10^{-34}\ \text{J·s} \), \( c = 3.0\times 10^{8}\ \text{m/s} \), and \( \lambda=532\ \text{nm}=532\times 10^{-9}\ \text{m} \).

Step2: Substitute values into the formula

First, calculate the numerator \( hc \): \( hc=(6.626\times 10^{-34}\ \text{J·s})\times(3.0\times 10^{8}\ \text{m/s}) = 1.9878\times 10^{-25}\ \text{J·m} \).

Then, divide by \( \lambda \): \( E=\frac{1.9878\times 10^{-25}\ \text{J·m}}{532\times 10^{-9}\ \text{m}} \).

Simplify the division: \( \frac{1.9878\times 10^{-25}}{532\times 10^{-9}}=\frac{1.9878}{532}\times 10^{-25 + 9}\approx0.003736\times 10^{-16}=3.74\times 10^{-19}\ \text{J} \).

Answer:

A. \( 3.74 \times 10^{-19}\ \text{J} \)