Question

what is the wavelength (in nm) of a photon if the energy is 7.35×10 - 19 j? (h = 6.626×10 - 34 j·s and c = 3.00×10 8 m/s) answer: nm

Explanation:

Step1: Recall energy - wavelength formula

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

Step2: Substitute given values

We are given $h = 6.626\times10^{-34}\ J\cdot s$, $c = 3.00\times10^{8}\ m/s$, and $E = 7.35\times10^{-19}\ J$.
Substitute these values into the formula: $\lambda=\frac{(6.626\times 10^{-34}\ J\cdot s)\times(3.00\times 10^{8}\ m/s)}{7.35\times 10^{-19}\ J}$.
First, calculate the numerator: $(6.626\times 10^{-34})\times(3.00\times 10^{8})=19.878\times10^{-26}\ J\cdot m = 1.9878\times 10^{-25}\ J\cdot m$.
Then, divide by the denominator: $\lambda=\frac{1.9878\times 10^{-25}\ J\cdot m}{7.35\times 10^{-19}\ J}=2.7045\times10^{-7}\ m$.

Step3: Convert to nanometers

Since $1\ m = 10^{9}\ nm$, then $\lambda=(2.7045\times 10^{-7}\ m)\times(10^{9}\ nm/m)=270.45\ nm$.

Answer:

$270.45\ nm$