In a hydrogen-like atom electron make transition from an energy level with quantum number to another with quantum number . If , the frequency of radiation emitted is proportional to: [2012]

Question

In a hydrogen-like atom electron make 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: [2012]

Smart Achievers · Accepted Answer

(4)

$Δ E = h ν$

$n ≫ 1$ or, $ν \propto \frac{1}{n^{3}}$

Solution

Q.
In a hydrogen-like atom electron make 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: [2012]

1 $\frac{1}{n}$

2 $\frac{1}{n^{2}}$

3 $\frac{1}{n^{3} / 2}$

4 $\frac{1}{n^{3}}$

Ans.
(4)

$Δ E = h ν$

$ν = \frac{Δ E}{h} = k [\frac{1}{{(n - 1)}^{2}} - \frac{1}{n^{2}}] = \frac{k (2 n - 1)}{n^{2} {(n - 1)}^{2}} \approx \frac{2 k}{n^{3}}$ or, $ν \propto \frac{1}{n^{3}}$

Want Us to Email you About Special Offers & Updates?

Solution

Q. In a hydrogen-like atom electron make 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: [2012]

1 1n

2 1n2

3 1n3/2

4 1n3

Ans. (4) ΔE=hν ν=ΔEh=k[1(n-1)2-1n2]=k(2n-1)n2(n-1)2≈2kn3 or, ν∝1n3