In a hydrogen atom the electron makes a transition from ( n + 1 ) t h level to the n t h level. If n 1 , the frequency of radiation emitted is proportional to :

Question

In a hydrogen atom the electron makes a transition from ( n + 1 ) t h level to the n t h level. If n >> 1 , the frequency of radiation emitted is proportional to :

TestHub · Accepted Answer

E n ​ = − n 2 R h c ​ E n + 1 ​ = − ( n + 1 ) 2 R h c ​ Δ E = E n + 1 ​ − E n ​ h v = R h c [ n 2 1 ​ − ( n + 1 ) 2 1 ​ ] v = R . c [ n 2 ( n + 1 ) 2 ( n + 1 ) 2 − n 2 ​ ] v = R . c [ n 2 ( n + 1 ) 2 1 + 2 n ​ ] n >> 1 ⇒ v = R . c [ n 2 × n 2 2 n ​ ] = n 3 2 R C ​ v ∞ n 3 1 ​

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