30.30 - Applications of Atomic Excitations and De-Excitations The figure below s

Question

30.30 - Applications of Atomic Excitations and De-Excitations The figure below shows the energy-level diagram for two hypothetical gaseous elements used to produce a laser. Energy is pumped from the ground state to the first level of element 1. Collisions between the two elements transfer the energy to a metastable state in element 2. What is the energy difference between the metastable state to one immediately below it? Collision transfers energy Metastable ?? First 17.53 eV15.60 ev Ground state Element 1 Element 2 Submit Answer Tries 0/10 What is the wavelength of the radiation resulting from the transiton? Submit Answer Tries 0/10 What wavelength is emitted if element 2 makes a direct transition from the metastable state to its ground state? Submit Answer Tries 0/10

Explanation / Answer

Energy difference between metastable state to the one immediately below it is 17.53eV- 15.60eV = 1.93eV

Now, 15.60eV = 15.60*1.6*10^-19 J = 2.5*10^-18 J .

So, from energy E = Planck's constant*frequency ;

2.5*10^-18 = 6.626*10^-34 * f

So, frequency f = 3.77*10^15 Hz

So, Wavelength of radiation resulting from the transition is 3*10^8 / 3.77*10^15 = 7.95*10^-8 m

Similarly, in case of direct transition from metastable state , 17.53eV*1.6*10^-19 J = 2.8*10^-18 J .

So, f = 2.8*10^-18 / 6.626*10^-34 = 4.2*10^15 Hz

So , Wavelength of radiation resulting from the direct transition from the metastable state to its ground state is 3*10^8 / 4.2*10^15 = 7.1*10^-8 m

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