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Question: When hydrogen like atom in excited state make a transition from excited state to ground state, most ...

When hydrogen like atom in excited state make a transition from excited state to ground state, most energetic photons have energy Emax = 52.224 eV and least energetic photons have energy Emin = 1.224 eV. Find the atomic number –

A

4

B

6

C

2

D

8

Answer

2

Explanation

Solution

Maximum energy is liberated for transition

En ® 1 and minimum energy for En ® En–1

Hence , E1n2−E1\frac{E_{1}}{n^{2}} - E_{1}= 52.224 eV … (1)

E1n2−E1(n−1)2\frac{E_{1}}{n^{2}} - \frac{E_{1}}{(n - 1)^{2}} = 1.224 eV … (2)

Solving (1) and (2) E1 = – 54.4 eV

E1 = −13.6Z212- \frac{13.6Z^{2}}{1^{2}}

Z = 2