Question

unit 3, quiz #1, frq #1 (3 points)
calculate the energy of the photon having the given wavelength (given verbally in class).
document all work and process for full credit. box your final answer.
651 nm

Explanation:

Step1: Convert wavelength to meters

Given wavelength \(\lambda = 651\ nm=651\times10^{- 9}\ m\) (since \(1\ nm = 10^{-9}\ m\)).

Step2: Use the formula \(E = hc/\lambda\)

where \(h = 6.626\times10^{-34}\ J\cdot s\) (Planck's constant) and \(c = 3\times10^{8}\ m/s\) (speed of light).
Substitute the values:
\(E=\frac{6.626\times 10^{-34}\times3\times 10^{8}}{651\times10^{-9}}\)
First, calculate the numerator: \(6.626\times 10^{-34}\times3\times 10^{8}=19.878\times10^{-26}\)
Then, divide by the denominator: \(\frac{19.878\times10^{-26}}{651\times10^{-9}}=\frac{19.878}{651}\times10^{-26 + 9}\)
\(\frac{19.878}{651}\approx0.0305\), and \(10^{-26 + 9}=10^{-17}\)
So \(E = 3.05\times10^{-19}\ J\)

Answer:

\(\boxed{3.05\times 10^{-19}\ J}\)