Question

question 17 of 30 how much energy does a 930 nm wave of light have? (the speed of light in a vacuum is 3.00 × 10⁸ m/s, and planck’s constant is 6.626 × 10⁻³⁴ j·s.) a. 4.68 × 10¹⁸ j b. 2.14 × 10⁻¹⁹ j c. 4.21 × 10³⁵ j d. 1.85 × 10⁻³¹ j

Explanation:

Step1: Recall the formula for photon energy

The energy \( E \) of a photon is given by \( E = h
u \), where \( h \) is Planck's constant and \(
u \) is the frequency. Also, the speed of light \( c = \lambda
u \), so \(
u=\frac{c}{\lambda} \). Substituting \(
u \) into the energy formula gives \( E=\frac{hc}{\lambda} \).

Step2: Convert wavelength to meters

The wavelength \( \lambda = 930\space nm \). Since \( 1\space nm = 10^{-9}\space m \), we have \( \lambda = 930\times 10^{-9}\space m=9.3\times 10^{-7}\space m \).

Step3: Plug in the values into the formula

We know \( h = 6.626\times 10^{-34}\space J\cdot s \), \( c = 3.00\times 10^{8}\space m/s \), and \( \lambda = 9.3\times 10^{-7}\space m \).

Substitute these into \( E=\frac{hc}{\lambda} \):

\[

$$\begin{align*} E&=\frac{(6.626\times 10^{-34}\space J\cdot s)(3.00\times 10^{8}\space m/s)}{9.3\times 10^{-7}\space m}\\ &=\frac{1.9878\times 10^{-25}\space J\cdot m}{9.3\times 10^{-7}\space m}\\ &\approx 2.14\times 10^{-19}\space J \end{align*}$$

\]

Answer:

B. \( 2.14 \times 10^{-19}\space J \)