Question

1. calculate the energy of a photon with a wavelength of 750 nm. a. 2.65 x 10^(-20) j b. 2.65 x 10^(-19) j c. 3.31 x 10^(-19) j d. 3.98 x 10^(-19) j. e. 2.25 x 10^(14) j

Explanation:

Step1: Recall the energy - wavelength formula

The energy of a photon is given by the formula $E = h
u=\frac{hc}{\lambda}$, where $h = 6.626\times10^{-34}\ J\cdot s$ (Planck's constant), $c= 3\times10^{8}\ m/s$ (speed of light), and $\lambda$ is the wavelength of the photon.

Step2: Convert the wavelength to SI units

The given wavelength $\lambda = 750\ nm=750\times10^{-9}\ m$.

Step3: Substitute the values into the formula

$E=\frac{hc}{\lambda}=\frac{(6.626\times 10^{-34}\ J\cdot s)\times(3\times 10^{8}\ m/s)}{750\times 10^{-9}\ m}$.
First, calculate the numerator: $(6.626\times 10^{-34})\times(3\times 10^{8})=19.878\times10^{-26}\ J\cdot m$.
Then, divide by the denominator: $E=\frac{19.878\times 10^{-26}\ J\cdot m}{750\times 10^{-9}\ m}=2.65\times 10^{-19}\ J$.

Answer:

B. $2.65\times 10^{-19}\ J$