In a hydrogen like atom electron makes transition from an energy level with quantum number n to another with quantum number (n - 1) . If n >> 1 , the frequency of radiation emitted is proportional to :

Correct answer: B. 1 n ^ 3 Δ E = h ν ν = Δ E h = k [ 1 (n - 1) ^ 2 - 1 n ^ 2 ] = k 2 n n ^ 2 (n - 1) ^ 2 2 k n ^ 3 ∝ 1 n ^ 3

JEE Main 20137 April

JEE Main 2013 · 7 April · Physics · Atomic Physics

In a hydrogen like atom electron makes transition from an energy...

In a hydrogen like atom electron makes transition from an energy level with quantum number

\text{n}

to another with quantum number \left(\text{n} - 1\right)

. If

\text{n >> 1}$, the frequency of radiation emitted is proportional to :

B. $\dfrac{1}{{\text{n}}^{3}}$

\Delta \text{E} = \text{h} ν

ν = \dfrac{\Delta \text{E}}{\text{h}} = \text{k} \left[\dfrac{1}{{\left(\text{n} - 1\right)}^{2}} - \dfrac{1}{{\text{n}}^{2}}\right] = \dfrac{\text{k} 2 \text{n}}{{\text{n}}^{2} {\left(\text{n} - 1\right)}^{2}}

\approx \dfrac{2 \text{k}}{{\text{n}}^{3}} ∝ \dfrac{1}{{\text{n}}^{3}}