QuestionAugust 10, 2025

A photon has the energy 5.55times 10^-19J What is this photon's wavelength in nanometers? A 358 nm B ) 590 nm C 3.58times 10^-7nm c D 222 nm

A photon has the energy 5.55times 10^-19J What is this photon's wavelength in nanometers? A 358 nm B ) 590 nm C 3.58times 10^-7nm c D 222 nm
A photon has the energy 5.55times 10^-19J What is this photon's wavelength in nanometers? A 358 nm B ) 590 nm C 3.58times 10^-7nm c D 222 nm

Solution
4.5(182 votes)

Answer

A 358 nm Explanation 1. Use the energy-wavelength relation The energy of a photon is given by E = \frac{hc}{\lambda}, where h is Planck's constant (6.626 \times 10^{-34} \, \text{J}\cdot\text{s}), c is the speed of light (3.00 \times 10^8 \, \text{m/s}), and \lambda is the wavelength. 2. Solve for wavelength \lambda Rearrange the formula to find \lambda: \lambda = \frac{hc}{E}. Substitute h = 6.626 \times 10^{-34} \, \text{J}\cdot\text{s}, c = 3.00 \times 10^8 \, \text{m/s}, and E = 5.55 \times 10^{-19} \, \text{J}. Calculate: \lambda = \frac{(6.626 \times 10^{-34})(3.00 \times 10^8)}{5.55 \times 10^{-19}} = 3.58 \times 10^{-7} \, \text{m}. 3. Convert meters to nanometers 1 \, \text{m} = 10^9 \, \text{nm}, so multiply by 10^9: 3.58 \times 10^{-7} \, \text{m} = 358 \, \text{nm}.

Explanation

1. Use the energy-wavelength relation<br /> The energy of a photon is given by $E = \frac{hc}{\lambda}$, where $h$ is Planck's constant ($6.626 \times 10^{-34} \, \text{J}\cdot\text{s}$), $c$ is the speed of light ($3.00 \times 10^8 \, \text{m/s}$), and $\lambda$ is the wavelength.<br />2. Solve for wavelength $\lambda$<br /> Rearrange the formula to find $\lambda$: $\lambda = \frac{hc}{E}$. Substitute $h = 6.626 \times 10^{-34} \, \text{J}\cdot\text{s}$, $c = 3.00 \times 10^8 \, \text{m/s}$, and $E = 5.55 \times 10^{-19} \, \text{J}$.<br /> Calculate: $\lambda = \frac{(6.626 \times 10^{-34})(3.00 \times 10^8)}{5.55 \times 10^{-19}} = 3.58 \times 10^{-7} \, \text{m}$.<br />3. Convert meters to nanometers<br /> $1 \, \text{m} = 10^9 \, \text{nm}$, so multiply by $10^9$: $3.58 \times 10^{-7} \, \text{m} = 358 \, \text{nm}$.
Click to rate:

Similar Questions