The following diagram shows the emission spectrum of a hydrogen atom,please answ

Question

The following diagram shows the emission spectrum of a hydrogen atom,please answer following questions.

Lyman Balmer Paschen a) Why does the emission spectrum consist of only certain discrete frequencies? Explain in one sentence. [lpt] (b) For the hydrogen atom, how does the adjacent energy gap change with increasing quantum number? Ipt] (e) Which microscopic system(s) also shows) the same pattern? Circle the correct one(s). [Ipt A. Particle-in-a-box B. Harmonic ic oscillator C. Rigid Rotator D. Anharmonic oscillator (d) Using the information provided in the above spectrum, calculate the transition energy between n = 3 and n 4 electronic states. Express the answer in Joules. [2pts]

Explanation / Answer

a. According to Planck's quantum theory, the energy releases in the form of small packets called quanta, hence the emission spectrum consists of only certain discrete frequencies.

b. For H-atom, En = -2.176*10-18/n2 J

As the quantum number (n) increases, the adjacent energy gap decreases.

c. Anharmonic oscillator

d. E4 - E3 = -2.176*10-18 (1/42 -1/32) J

= 1.06*10-19 J

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