Question

what is the wavelength (in nm) of a photon if the energy is 7.65×10^(-19) j? (h = 6.626×10^(-34) j·s and c = 3.00×10^8 m/s)

Explanation:

Step1: Recall energy - wavelength formula

The energy of a photon is given by $E = \frac{hc}{\lambda}$, where $E$ is energy, $h$ is Planck's constant, $c$ is the speed of light, and $\lambda$ is the wavelength. We can re - arrange this formula to solve for $\lambda$: $\lambda=\frac{hc}{E}$.

Step2: Substitute the given values

We are given $h = 6.626\times10^{-34}\ J\cdot s$, $c = 3.00\times 10^{8}\ m/s$, and $E=7.65\times 10^{-19}\ J$.
$\lambda=\frac{(6.626\times 10^{-34}\ J\cdot s)\times(3.00\times 10^{8}\ m/s)}{7.65\times 10^{-19}\ J}$

Step3: Calculate the wavelength in meters

First, calculate the numerator: $(6.626\times 10^{-34})\times(3.00\times 10^{8}) = 19.878\times10^{-26}\ J\cdot m/s$.
Then, divide by the energy: $\lambda=\frac{19.878\times 10^{-26}\ J\cdot m/s}{7.65\times 10^{-19}\ J}=2.6\times10^{-7}\ m$.

Step4: Convert the wavelength to nanometers

Since $1\ m = 10^{9}\ nm$, then $\lambda=(2.6\times 10^{-7}\ m)\times(10^{9}\ nm/m)=260\ nm$.

Answer:

260