Question

3. An atom of some element X has three electronic transitions, A, B, and C. Suppose that it has been found that the wavelength for transition A is 407.7 nm and that for B is 690.0 nm. (a) What is the energy in J) for a photon given off in transition C? (b) What is the wavelength (in nm) for transition C? Energy

Answer 1

From the figure, it is clear that Energy of transition C = Energy of transition A + Energy of transition B

Energy of transition A = hc / $\lambda$ , where h is planck's constant, c is velocity of light and $\lambda$ is wavelength in meters

Using the given values , we get:'

Energy of A = 6.625 * 10^-34 * 3 * 10⁸ / (407.7 * 10^-9) = 4.88 * 10^-19J

Energy of transition B = 6.625 * 10^-34 * 3 * 10⁸ / (690 * 10^-9) = 2.88 * 10^-19J

Energy of C = 4.88 * 10^-19+ 2.88 * 10^-19= 7.76 * 10^-19 J

Using the relation : Energy = hc / $\lambda$

7.76 * 10^-19 = 6.625 * 10^-34 * 3 * 10⁸ / $\lambda$

Solving for wavelength, we get: $\lambda$ = 2.56 * 10^-7 m = 256 nm