Question

Have you ever chewed on a wintergreen mint in front of a mirror in the dark? If you have, you may have noticed some sparks of light coming out of your mouth as you chewed on the candy; and, without knowing it, you have experienced a physical phenomenon called triboluminescence. In this problem you will analyze some of the key elements of triboluminescence in wintergreen candies. When you break a sugar crystal with your teeth, energetic electrons, released by the broken chemical bonds, collide with nitrogen molecules in the air. As a result of these collisions, the electrons in the nitrogen molecules jump to a state of higher energy; when they decay to their ground state, radiation is emitted. Part A Imagine that an electron in an excited state in a nitrogen molecule decays to its ground state, emitting a photon with a frequency of 8.88×1014 Hz . What is the change in energy, ΔE, that the electron undergoes to decay to its ground state?

Answer 1

Answer:

$\Delta E = -5.89\cdot 10^{-19} J$

Explanation:

The change in energy of the electron that undergoes the decay is equal to the energy of the photon, which is given by:

$\Delta E=hf$

where

h is the Planck constant

f is the frequency of the Photon

Here we have

$f=8.88\cdot 10^{14}Hz$

Substituting into the formula, we find

$\Delta E=(6.63\cdot 10^{-34} Js)(8.88\cdot 10^{14}Hz)=5.89\cdot 10^{-19} J$

and since the electron decays from a higher energy level to the ground state, its change in energy will be negative:

$\Delta E = -5.89\cdot 10^{-19} J$