calculate the energy of the violet light emitted by a hydrogen atom with a wavelength of 410.1…

calculate the energy of the violet light emitted by a hydrogen atom with a wavelength of 410.1 nm.\n\n$9.118\times10^{-49}\text{ j}$\n\n$5.271\times10^{-19}\text{ j}$\n\n$2.717\times10^{-40}\text{ j}$\n\n$8.146\times10^{-32}\text{ j}$\n\n$4.844\times10^{-19}\text{ j}$

calculate the energy of the violet light emitted by a hydrogen atom with a wavelength of 410.1 nm.\n\n$9.118\times10^{-49}\text{ j}$\n\n$5.271\times10^{-19}\text{ j}$\n\n$2.717\times10^{-40}\text{ j}$\n\n$8.146\times10^{-32}\text{ j}$\n\n$4.844\times10^{-19}\text{ j}$

Answer

Explanation:

Step1: Convert wavelength to meters

Convert 410.1 nm to m. Since 1 nm = 10⁻⁹ m, then $\lambda=410.1\times10^{-9}\text{ m}$.

Step2: Use the energy - wavelength formula

The formula for the energy of a photon is $E = h\frac{c}{\lambda}$, where $h = 6.626\times10^{-34}\text{ J}\cdot\text{s}$ (Planck's constant) and $c = 3\times10^{8}\text{ m/s}$ (speed of light). $E=\frac{6.626\times 10^{-34}\text{ J}\cdot\text{s}\times3\times 10^{8}\text{ m/s}}{410.1\times10^{-9}\text{ m}}$ $E=\frac{19.878\times10^{-26}}{410.1\times10^{-9}}\text{ J}$ $E = 4.847\times10^{-19}\text{ J}\approx4.844\times10^{-19}\text{ J}$

Answer:

$4.844\times 10^{-19}\text{ J}$