Question

An atom emits a photon of red light of wavelength 400 nm during the transition from energy level Z to X, and emits a photon of violet light of wavelength 700 nm during the transition from energy level Y to X. What is the wavelength of the photon emitted during the transition from Z to Y?

Answer 1

Given:

An atom emits a photon of red light of wavelength 400 nm during the transition from energy level Z to X, and emits a photon of violet light of wavelength 700 nm during the transition from energy level Y to X.

To Find:

What is the wavelength of the photon emitted during the transition from Z to Y?

Solution:

Whenever a electron jumps from one energy level to another , it emits a photon of energy which is exactly equal to the difference between the energy level of 2 orbits.

According to Plank's theory ,

energy of photon is directly proportional to its frequency.

$E \alpha \nu\\E = h \nu$

h - plank's constant .

$\nu = \frac{c}{ \lambda}$

where c is speed of light and lambda is wavelength of photon.

$E \alpha \frac{1}{\lambda}$

Energy difference between energy level of X and Z = $\delta E = E_{z} - E_{x}$

$E_{zx} = E_{zy} + E_{yx}$

$E_{zx} = \frac{hc}{\lambda}\\E_{zx} = \frac{hc}{400}$

similarily,

$E_{xy} = \frac{hc}{700}$

$\frac{hc}{400} = \frac{hc}{700} + \frac{hc}{\lambda} \\\lambda = 933.333 nm$

The wavelength of photon emitted during the transition from Z and Y is 933.33 nm.