For a particular molecule the vibrational energy levels are spaced 0.15 eV apart. The wavelength emitted during a transition from one level to a lower level is
A) $6.5 \mu \mathrm { m }$
B) $8.3 \mu \mathrm { m }$
C) $65 \mathrm {~nm}$
D) $83 \mathrm {~nm}$

Question

Quizplus · Accepted Answer

The energy difference between the levels is given as 0.15 eV. To find the wavelength of the emitted photon, we can use the equation $E = \frac{hc}{\lambda}$, where $E$ is the energy in joules, $h$ is Planck's constant ($6.626 \times 10^{-34} \, \mathrm{m^2 kg / s}$), $c$ is the speed of light ($3.00 \times 10^8 \, \mathrm{m/s}$), and $\lambda$ is the wavelength in meters. First, convert the energy from eV to joules (1 eV = $1.602 \times 10^{-19}$ joules). Thus, $0.15 \, \mathrm{eV} = 0.15 \times 1.602 \times 10^{-19} \, \mathrm{J}$. Then, rearrange the equation to solve for $\lambda$: $\lambda = \frac{hc}{E}$. Plugging in the values, we find $\lambda \approx 8.3 \mu \mathrm{m}$.

For a Particular Molecule the Vibrational Energy Levels Are Spaced 6.5μm6.5 \mu \mathrm { m }6.5μm

For a Particular Molecule the Vibrational Energy Levels Are Spaced $6.5 \mu \mathrm { m }$