Question

the wavelength of a photon that has an energy of 7.85 x 10^(-19) j is ? blank 1:

Explanation:

Step1: Recall energy - wavelength formula

The energy of a photon is given by $E = h
u=\frac{hc}{\lambda}$, where $E$ is energy, $h = 6.626\times10^{-34}\ J\cdot s$ (Planck's constant), $c= 3\times 10^{8}\ m/s$ (speed of light) and $\lambda$ is wavelength. We need to solve for $\lambda$, so $\lambda=\frac{hc}{E}$.

Step2: Substitute the values

Substitute $h = 6.626\times10^{-34}\ J\cdot s$, $c = 3\times 10^{8}\ m/s$ and $E=7.85\times 10^{-19}\ J$ into the formula.
$\lambda=\frac{6.626\times 10^{-34}\ J\cdot s\times3\times 10^{8}\ m/s}{7.85\times 10^{-19}\ J}$

Step3: Calculate the result

First, calculate the numerator: $6.626\times 10^{-34}\times3\times 10^{8}=19.878\times10^{-26}=1.9878\times 10^{-25}\ J\cdot m$.
Then, $\lambda=\frac{1.9878\times 10^{-25}\ J\cdot m}{7.85\times 10^{-19}\ J}=2.53\times 10^{-7}\ m$.

Answer:

$2.53\times 10^{-7}\ m$