Question

what is the wavelength (in nm) of a photon if the energy is 5.76e - 19 j? (h = 6.626×10^(-34) j·s) answer: nm

Explanation:

Step1: Recall energy - wavelength formula

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

Step2: Substitute the given values

Substitute $h = 6.626\times10^{-34}\ J\cdot s$, $c = 3\times10^{8}\ m/s$, and $E = 5.76\times10^{-19}\ J$ into the formula.
$\lambda=\frac{6.626\times10^{-34}\ J\cdot s\times3\times10^{8}\ m/s}{5.76\times10^{-19}\ J}$
First, calculate the numerator: $6.626\times10^{-34}\times3\times10^{8}=19.878\times10^{-26}\ J\cdot m = 1.9878\times10^{-25}\ J\cdot m$.
Then, divide by the denominator: $\lambda=\frac{1.9878\times10^{-25}\ J\cdot m}{5.76\times10^{-19}\ J}= 3.45\times10^{-7}\ m$.

Step3: Convert to nanometers

Since $1\ m = 10^{9}\ nm$, then $\lambda=3.45\times10^{-7}\ m\times10^{9}\ nm/m = 345\ nm$.

Answer:

345 nm